Problems 201 to 300

Table 4.629: First order ode linear in derivative


#	ODE	Mathematica	Maple	Sympy

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

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

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

662	\[ {} y^{\prime } = x +y \]	✓	✓	✓

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

664	\[ {} y^{\prime } = x -y \]	✓	✓	✓

665	\[ {} y^{\prime } = y-x +1 \]	✓	✓	✓

666	\[ {} y^{\prime } = x -y+1 \]	✓	✓	✓

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

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

669	\[ {} y^{\prime } = 2 x^{2} y^{2} \]	✓	✓	✓

670	\[ {} y^{\prime } = x \ln \left (y\right ) \]	✓	✓	✓

671	\[ {} y^{\prime } = y^{{1}/{3}} \]	✓	✓	✗

672	\[ {} y^{\prime } = y^{{1}/{3}} \]	✓	✓	✓

673	\[ {} y y^{\prime } = x -1 \]	✓	✓	✓

674	\[ {} y y^{\prime } = x -1 \]	✓	✓	✓

675	\[ {} y^{\prime } = \ln \left (1+y^{2}\right ) \]	✓	✓	✓

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

677	\[ {} y^{\prime }+2 x y = 0 \]	✓	✓	✓

678	\[ {} y^{\prime }+2 x y^{2} = 0 \]	✓	✓	✓

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

680	\[ {} \left (1+x \right ) y^{\prime } = 4 y \]	✓	✓	✓

681	\[ {} 2 \sqrt {x}\, y^{\prime } = \sqrt {1-y^{2}} \]	✓	✓	✓

682	\[ {} y^{\prime } = 3 \sqrt {x y} \]	✓	✓	✓

683	\[ {} y^{\prime } = 4 \left (x y\right )^{{1}/{3}} \]	✓	✓	✗

684	\[ {} y^{\prime } = 2 x \sec \left (y\right ) \]	✓	✓	✓

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

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

687	\[ {} y^{\prime } = x y^{3} \]	✓	✓	✓

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

689	\[ {} y^{\prime } = \frac {1+\sqrt {x}}{1+\sqrt {y}} \]	✓	✓	✗

690	\[ {} y^{\prime } = \frac {\left (x -1\right ) y^{5}}{x^{2} \left (2 y^{3}-y\right )} \]	✓	✓	✗

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

692	\[ {} y^{\prime } = 1+x +y+x y \]	✓	✓	✓

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

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

695	\[ {} y^{\prime } = 3 x^{2} \left (1+y^{2}\right ) \]	✓	✓	✓

696	\[ {} 2 y y^{\prime } = \frac {x}{\sqrt {x^{2}-16}} \]	✓	✓	✓

697	\[ {} y^{\prime } = 4 x^{3} y-y \]	✓	✓	✓

698	\[ {} y^{\prime }+1 = 2 y \]	✓	✓	✓

699	\[ {} \tan \left (x \right ) y^{\prime } = y \]	✓	✓	✓

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

701	\[ {} y^{\prime } = 2 x y^{2}+3 x^{2} y^{2} \]	✓	✓	✓

702	\[ {} y^{\prime } = 6 \,{\mathrm e}^{2 x -y} \]	✓	✓	✓

703	\[ {} 2 \sqrt {x}\, y^{\prime } = \cos \left (y\right )^{2} \]	✓	✓	✓

704	\[ {} y^{\prime }+y = 2 \]	✓	✓	✓

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

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

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

708	\[ {} x y^{\prime }+2 y = 3 x \]	✓	✓	✓

709	\[ {} 2 x y^{\prime }+y = 10 \sqrt {x} \]	✓	✓	✓

710	\[ {} 2 x y^{\prime }+y = 10 \sqrt {x} \]	✓	✓	✓

711	\[ {} 3 x y^{\prime }+y = 12 x \]	✓	✓	✓

712	\[ {} x y^{\prime }-y = x \]	✓	✓	✓

713	\[ {} 2 x y^{\prime }-3 y = 9 x^{3} \]	✓	✓	✓

714	\[ {} x y^{\prime }+y = 3 x y \]	✓	✓	✓

715	\[ {} x y^{\prime }+3 y = 2 x^{5} \]	✓	✓	✓

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

717	\[ {} x y^{\prime }-3 y = x^{3} \]	✓	✓	✓

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

719	\[ {} y^{\prime } = \left (1-y\right ) \cos \left (x \right ) \]	✓	✓	✓

720	\[ {} \left (1+x \right ) y^{\prime }+y = \cos \left (x \right ) \]	✓	✓	✓

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

722	\[ {} y^{\prime }+\cot \left (x \right ) y = \cos \left (x \right ) \]	✓	✓	✓

723	\[ {} y^{\prime } = 1+x +y+x y \]	✓	✓	✓

724	\[ {} x y^{\prime } = 3 y+x^{4} \cos \left (x \right ) \]	✓	✓	✓

725	\[ {} y^{\prime } = 2 x y+3 x^{2} {\mathrm e}^{x^{2}} \]	✓	✓	✓

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

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

728	\[ {} \left (x^{2}+1\right ) y^{\prime }+3 x^{3} y = 6 x \,{\mathrm e}^{-\frac {3 x^{2}}{2}} \]	✓	✓	✗

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

730	\[ {} 2 x y y^{\prime } = x^{2}+y^{2} \]	✓	✓	✓

731	\[ {} x y^{\prime } = y+2 \sqrt {x y} \]	✓	✓	✓

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

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

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

735	\[ {} x y^{2} y^{\prime } = x^{3}+y^{3} \]	✓	✓	✓

736	\[ {} y^{\prime } x^{2} = x y+x^{2} {\mathrm e}^{\frac {y}{x}} \]	✓	✓	✗

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

738	\[ {} x y y^{\prime } = x^{2}+3 y^{2} \]	✓	✓	✓

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

740	\[ {} x y y^{\prime } = y^{2}+x \sqrt {4 x^{2}+y^{2}} \]	✓	✓	✗

741	\[ {} x y^{\prime } = y+\sqrt {x^{2}+y^{2}} \]	✓	✓	✓

742	\[ {} y y^{\prime }+x = \sqrt {x^{2}+y^{2}} \]	✓	✓	✓

743	\[ {} x \left (x +y\right ) y^{\prime }+y \left (3 x +y\right ) = 0 \]	✓	✓	✓

744	\[ {} y^{\prime } = \sqrt {x +y+1} \]	✓	✓	✓

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

746	\[ {} \left (x +y\right ) y^{\prime } = 0 \]	✓	✓	✓

747	\[ {} y^{\prime } x^{2}+2 x y = 5 y^{3} \]	✓	✓	✓

748	\[ {} y^{2} y^{\prime }+2 x y^{3} = 6 x \]	✓	✓	✓

749	\[ {} y^{\prime } = y+y^{3} \]	✓	✓	✓

750	\[ {} y^{\prime } x^{2}+2 x y = 5 y^{4} \]	✓	✓	✓

751	\[ {} x y^{\prime }+6 y = 3 x y^{{4}/{3}} \]	✓	✓	✓

752	\[ {} 2 x y^{\prime }+y^{3} {\mathrm e}^{-2 x} = 2 x y \]	✓	✓	✓

753	\[ {} y^{2} \left (x y^{\prime }+y\right ) \sqrt {x^{4}+1} = x \]	✓	✓	✓

754	\[ {} 3 y^{2} y^{\prime }+y^{3} = {\mathrm e}^{-x} \]	✓	✓	✓

755	\[ {} 3 x y^{2} y^{\prime } = 3 x^{4}+y^{3} \]	✓	✓	✓

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

757	\[ {} 2 x \sin \left (y\right ) \cos \left (y\right ) y^{\prime } = 4 x^{2}+\sin \left (y\right )^{2} \]	✓	✓	✓

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

4.9.3 Problems 201 to 300