4.5.7 Problems 601 to 700

Table 4.661: Second ODE non-homogeneous ODE

#

ODE

Mathematica

Maple

Sympy

4488

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{2 x} \sin \left (2 x \right ) x \]

4497

\[ {} -y+y^{\prime \prime } = \frac {1}{x}-\frac {2}{x^{3}} \]

4498

\[ {} -y+y^{\prime \prime } = \frac {1}{\sinh \left (x \right )} \]

4499

\[ {} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{x}}{x} \]

4500

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{x}\right ) \]

4501

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = \sin \left ({\mathrm e}^{-x}\right ) \]

4502

\[ {} y^{\prime \prime }+y = \sec \left (x \right )^{3} \]

4503

\[ {} -y+y^{\prime \prime } = \frac {1}{\sqrt {1-{\mathrm e}^{2 x}}} \]

4504

\[ {} -y+y^{\prime \prime } = {\mathrm e}^{-2 x} \sin \left ({\mathrm e}^{-x}\right ) \]

4505

\[ {} y+2 y^{\prime }+y^{\prime \prime } = 15 \,{\mathrm e}^{-x} \sqrt {1+x} \]

4506

\[ {} y^{\prime \prime }+4 y = 2 \tan \left (x \right ) \]

4507

\[ {} y^{\prime \prime }-2 y^{\prime }+y = \frac {{\mathrm e}^{2 x}}{\left ({\mathrm e}^{x}+1\right )^{2}} \]

4508

\[ {} y^{\prime \prime }+y^{\prime } = \frac {1}{{\mathrm e}^{x}+1} \]

4509

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+y = \ln \left (x \right ) \]

4510

\[ {} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y = \frac {5 \ln \left (x \right )}{x^{2}} \]

4512

\[ {} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y = x \]

4514

\[ {} y^{\prime \prime }+4 y^{\prime }+3 y = 60 \cos \left (3 t \right ) \]

4515

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 9 \,{\mathrm e}^{-2 t} \]

4516

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 2 t^{2}+1 \]

4517

\[ {} y^{\prime \prime }+4 y = 8 \sin \left (2 t \right ) \]

4518

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 4 \,{\mathrm e}^{-t}+2 \,{\mathrm e}^{t} \]

4519

\[ {} y^{\prime \prime }-2 y^{\prime }+2 y = 8 \sin \left (t \right ) {\mathrm e}^{-t} \]

4520

\[ {} y^{\prime \prime }-2 y^{\prime }+5 y = 8 \,{\mathrm e}^{t} \sin \left (2 t \right ) \]

4521

\[ {} y^{\prime \prime }+y^{\prime }-2 y = 54 t \,{\mathrm e}^{-2 t} \]

4522

\[ {} y^{\prime \prime }-y^{\prime }-2 y = 9 \,{\mathrm e}^{2 t} \operatorname {Heaviside}\left (t -1\right ) \]

4523

\[ {} y^{\prime \prime }+2 y^{\prime }+y = 2 \sin \left (t \right ) \operatorname {Heaviside}\left (t -\pi \right ) \]

4524

\[ {} y^{\prime \prime }+4 y = 8 \operatorname {Heaviside}\left (t -\pi \right ) \sin \left (2 t \right ) \]

4525

\[ {} y^{\prime \prime }+4 y = 8 \left (t^{2}+t -1\right ) \operatorname {Heaviside}\left (t -2\right ) \]

4526

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{t} \operatorname {Heaviside}\left (t -2\right ) \]

4527

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = \delta \left (t -2\right ) \]

4528

\[ {} y^{\prime \prime }+4 y = 4 \operatorname {Heaviside}\left (t -\pi \right )+2 \delta \left (t -\pi \right ) \]

5716

\[ {} y^{\prime \prime } = x +\sin \left (x \right ) \]

5717

\[ {} y^{\prime \prime } = \operatorname {c1} \cos \left (a x \right )+\operatorname {c2} \sin \left (b x \right ) \]

5718

\[ {} y^{\prime \prime } = x \,{\mathrm e}^{x} \]

5719

\[ {} y^{\prime \prime } = \operatorname {c1} \,{\mathrm e}^{a x}+\operatorname {c2} \,{\mathrm e}^{-b x} \]

5722

\[ {} y^{\prime \prime }+y = a x \]

5723

\[ {} y^{\prime \prime }+y = a \cos \left (b x \right ) \]

5724

\[ {} y^{\prime \prime }+y = 8 \cos \left (x \right ) \cos \left (2 x \right ) \]

5725

\[ {} y^{\prime \prime }+y = \sec \left (x \right ) \]

5726

\[ {} y^{\prime \prime }+y = a \sin \left (b x \right ) \]

5727

\[ {} y^{\prime \prime }+y = \sin \left (a x \right ) \sin \left (b x \right ) \]

5728

\[ {} y^{\prime \prime }+y = 4 x \sin \left (x \right ) \]

5729

\[ {} y^{\prime \prime }+y = x \left (\cos \left (x \right )-x \sin \left (x \right )\right ) \]

5730

\[ {} y^{\prime \prime }+y = \tan \left (x \right )^{2} \]

5731

\[ {} y^{\prime \prime }+y = {\mathrm e}^{-x} \]

5732

\[ {} y^{\prime \prime }+y = {\mathrm e}^{x} \left (x^{2}-1\right ) \]

5733

\[ {} y^{\prime \prime }+y = \sin \left (2 x \right ) {\mathrm e}^{x} \]

5734

\[ {} y^{\prime \prime }+y = {\mathrm e}^{2 x} \cos \left (x \right ) \]

5736

\[ {} -2 y+y^{\prime \prime } = 4 x^{2} {\mathrm e}^{x^{2}} \]

5738

\[ {} y^{\prime \prime }+4 y = x \sin \left (x \right )^{2} \]

5739

\[ {} y^{\prime \prime }+4 y = 2 \tan \left (x \right ) \]

5740

\[ {} y^{\prime \prime }+4 y = 2 \tan \left (x \right ) \]

5741

\[ {} -a^{2} y+y^{\prime \prime } = 1+x \]

5742

\[ {} y^{\prime \prime } = a x +b y \]

5743

\[ {} y^{\prime \prime }+a^{2} y = x^{2}+x +1 \]

5744

\[ {} y^{\prime \prime }+a^{2} y = \cos \left (b x \right ) \]

5745

\[ {} y^{\prime \prime }+a^{2} y = \cot \left (a x \right ) \]

5746

\[ {} y^{\prime \prime }+a^{2} y = \sin \left (b x \right ) \]

5774

\[ {} y^{\prime \prime }-2 y^{\prime }+y = \left (x -6\right ) x^{2} \]

5775

\[ {} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \]

5776

\[ {} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \left (3 x^{2}+2 x +1\right ) \]

5777

\[ {} y^{\prime \prime }-2 y^{\prime }+y = {\mathrm e}^{x} \sin \left (x \right ) \]

5778

\[ {} y+2 y^{\prime }+y^{\prime \prime } = 3 \,{\mathrm e}^{2 x}+x^{2}-\cos \left (x \right ) \]

5779

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 8 x^{2} {\mathrm e}^{3 x} \]

5780

\[ {} y^{\prime \prime }-2 y^{\prime }+y = 50 \cosh \left (x \right ) \cos \left (x \right ) \]

5782

\[ {} y+2 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{-x} \cos \left (x \right ) \]

5784

\[ {} y^{\prime \prime }+2 y^{\prime }+5 y = 8 \sinh \left (x \right ) \]

5786

\[ {} \csc \left (a \right )^{2} y-2 \tan \left (a \right ) y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x \tan \left (a \right )} x^{2} \]

5788

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = \cos \left (a x \right ) \]

5789

\[ {} y^{\prime \prime }+3 y^{\prime }+2 y = {\mathrm e}^{x}+\sin \left (x \right ) \]

5790

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = 2 \,{\mathrm e}^{-x}+x^{2} \]

5791

\[ {} y^{\prime \prime }-3 y^{\prime }+2 y = {\mathrm e}^{a x} x \]

5793

\[ {} -4 y-3 y^{\prime }+y^{\prime \prime } = 10 \cos \left (2 x \right ) \]

5795

\[ {} 4 y-4 y^{\prime }+y^{\prime \prime } = {\mathrm e}^{2 x} \cos \left (x \right )^{2} \]

5797

\[ {} 5 y+4 y^{\prime }+y^{\prime \prime } = \sin \left (x \right ) \]

5800

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = 4 x^{2} {\mathrm e}^{x} \]

5801

\[ {} y^{\prime \prime }-5 y^{\prime }+6 y = {\mathrm e}^{a x} \]

5803

\[ {} y^{\prime \prime }+6 y^{\prime }+9 y = \cosh \left (x \right ) {\mathrm e}^{-3 x} \]

5805

\[ {} 12 y-7 y^{\prime }+y^{\prime \prime } = x \]

5807

\[ {} 16 y+8 y^{\prime }+y^{\prime \prime } = 4 \,{\mathrm e}^{x}-{\mathrm e}^{2 x} \]

5809

\[ {} 20 y-9 y^{\prime }+y^{\prime \prime } = x^{2} {\mathrm e}^{3 x} \]

5811

\[ {} y b^{2}+2 a y^{\prime }+y^{\prime \prime } = c \sin \left (k x \right ) \]

5812

\[ {} y^{\prime \prime }-2 a y^{\prime }+a^{2} y = {\mathrm e}^{x} \]

5815

\[ {} b y+a y^{\prime }+y^{\prime \prime } = f \left (x \right ) \]

5833

\[ {} -\left (-4 x^{2}+3\right ) y-4 x y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x^{2}} \]

5841

\[ {} x y-x^{2} y^{\prime }+y^{\prime \prime } = x \]

5854

\[ {} 3 y+2 \cot \left (x \right ) y^{\prime }+y^{\prime \prime } = {\mathrm e}^{x} \csc \left (x \right ) \]

5862

\[ {} \left (\cot \left (x \right )+\csc \left (x \right )\right ) y^{\prime }+y^{\prime \prime } = 1+a \csc \left (x \right ) \]

5867

\[ {} -y \cos \left (x \right )-y^{\prime } \sin \left (x \right )+y^{\prime \prime } = a -x +x \ln \left (x \right ) \]

5874

\[ {} -y+2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = \left (1+x \right ) \sec \left (x \right ) \]

5878

\[ {} -\left (a^{2}+1\right ) y-2 \tan \left (x \right ) y^{\prime }+y^{\prime \prime } = \sin \left (x \right ) \]

5894

\[ {} x y^{\prime \prime }+y^{\prime } = x^{n} \]

5902

\[ {} -x y+2 y^{\prime }+x y^{\prime \prime } = {\mathrm e}^{x} \]

5926

\[ {} x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y = x^{2}-x -1 \]

5935

\[ {} -8 x^{3} y-\left (2 x^{2}+1\right ) y^{\prime }+x y^{\prime \prime } = 4 x^{3} {\mathrm e}^{-x^{2}} \]

5940

\[ {} -y+x y^{\prime }+\left (1-x \right ) y^{\prime \prime } = \left (1-x \right )^{2} \]

5958

\[ {} x^{2} y^{\prime \prime } = b x +a \]

5965

\[ {} -\left (-x^{2}+2\right ) y+x^{2} y^{\prime \prime } = x^{4} \]

5977

\[ {} x^{2} y^{\prime \prime }+x y^{\prime }-y = x^{2} a \]

5978

\[ {} x^{2} y^{\prime \prime }-x y^{\prime }+y = x^{2} \left (x +3\right ) \]