Problems 5601 to 5700

Table 4.951: First order ode linear in derivative


#	ODE	Mathematica	Maple	Sympy

15682	\[ {} y^{\prime } = -x \sqrt {1-y^{2}} \]	✓	✓	✓

15683	\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]	✓	✓	✓

15684	\[ {} y^{\prime } = 3 x +1 \]	✓	✓	✓

15685	\[ {} y^{\prime } = x +\frac {1}{x} \]	✓	✓	✓

15686	\[ {} y^{\prime } = 2 \sin \left (x \right ) \]	✓	✓	✓

15687	\[ {} y^{\prime } = x \sin \left (x \right ) \]	✓	✓	✓

15688	\[ {} y^{\prime } = \frac {1}{x -1} \]	✓	✓	✓

15689	\[ {} y^{\prime } = \frac {1}{x -1} \]	✓	✓	✓

15690	\[ {} y^{\prime } = \frac {1}{x^{2}-1} \]	✓	✓	✓

15691	\[ {} y^{\prime } = \frac {1}{x^{2}-1} \]	✓	✓	✓

15692	\[ {} y^{\prime } = \tan \left (x \right ) \]	✓	✓	✓

15693	\[ {} y^{\prime } = \tan \left (x \right ) \]	✓	✓	✓

15694	\[ {} y^{\prime } = 3 y \]	✓	✓	✓

15695	\[ {} y^{\prime } = 1-y \]	✓	✓	✓

15696	\[ {} y^{\prime } = 1-y \]	✓	✓	✓

15697	\[ {} y^{\prime } = x \,{\mathrm e}^{y-x^{2}} \]	✓	✓	✓

15698	\[ {} y^{\prime } = \frac {y}{x} \]	✓	✓	✓

15699	\[ {} y^{\prime } = \frac {2 x}{y} \]	✓	✓	✓

15700	\[ {} y^{\prime } = -2 y+y^{2} \]	✗	✓	✓

15701	\[ {} y^{\prime } = x +x y \]	✓	✓	✓

15702	\[ {} x \,{\mathrm e}^{y}+y^{\prime } = 0 \]	✓	✓	✓

15703	\[ {} y-x^{2} y^{\prime } = 0 \]	✓	✓	✓

15704	\[ {} 2 y y^{\prime } = 1 \]	✓	✓	✓

15705	\[ {} 2 y y^{\prime } x +y^{2} = -1 \]	✓	✓	✓

15706	\[ {} y^{\prime } = \frac {1-x y}{x^{2}} \]	✓	✓	✓

15707	\[ {} y^{\prime } = -\frac {y \left (y+2 x \right )}{x \left (2 y+x \right )} \]	✓	✓	✓

15708	\[ {} y^{\prime } = \frac {y^{2}}{1-x y} \]	✓	✓	✓

15709	\[ {} y^{\prime } = 4 y+1 \]	✓	✓	✓

15710	\[ {} y^{\prime } = 2+x y \]	✓	✓	✓

15711	\[ {} y^{\prime } = \frac {y}{x} \]	✓	✓	✓

15712	\[ {} y^{\prime } = \frac {y}{x -1}+x^{2} \]	✓	✓	✓

15713	\[ {} y^{\prime } = \frac {y}{x}+\sin \left (x^{2}\right ) \]	✓	✓	✓

15714	\[ {} y^{\prime } = \frac {2 y}{x}+{\mathrm e}^{x} \]	✓	✓	✓

15715	\[ {} y^{\prime } = y \cot \left (x \right )+\sin \left (x \right ) \]	✓	✓	✓

15716	\[ {} x -y y^{\prime } = 0 \]	✓	✓	✓

15717	\[ {} y-x y^{\prime } = 0 \]	✓	✓	✓

15718	\[ {} x y^{\prime }+x^{2}-y = 0 \]	✓	✓	✓

15719	\[ {} x y \left (1-y\right )-2 y^{\prime } = 0 \]	✓	✓	✗

15720	\[ {} x \left (1-y^{3}\right )-3 y^{2} y^{\prime } = 0 \]	✓	✓	✓

15721	\[ {} \left (2 x -1\right ) y+x \left (1+x \right ) y^{\prime } = 0 \]	✓	✓	✓

15722	\[ {} y^{\prime } = \frac {1}{x -1} \]	✓	✓	✓

15723	\[ {} y^{\prime } = x +y \]	✓	✓	✓

15724	\[ {} y^{\prime } = \frac {y}{x} \]	✓	✓	✓

15725	\[ {} y^{\prime } = \frac {y}{x} \]	✓	✓	✓

15726	\[ {} y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x} \]	✓	✓	✓

15727	\[ {} y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x} \]	✓	✓	✓

15728	\[ {} y^{\prime } = \frac {y}{-x^{2}+1}+\sqrt {x} \]	✓	✓	✗

15729	\[ {} y^{\prime } = y^{2} \]	✓	✓	✓

15730	\[ {} y^{\prime } = y^{2} \]	✓	✓	✗

15731	\[ {} y^{\prime } = y^{2} \]	✓	✓	✓

15732	\[ {} y^{\prime } = y^{3} \]	✓	✓	✓

15733	\[ {} y^{\prime } = y^{3} \]	✓	✓	✗

15734	\[ {} y^{\prime } = y^{3} \]	✓	✓	✓

15735	\[ {} y^{\prime } = -\frac {3 x^{2}}{2 y} \]	✓	✓	✓

15736	\[ {} y^{\prime } = -\frac {3 x^{2}}{2 y} \]	✓	✓	✓

15737	\[ {} y^{\prime } = -\frac {3 x^{2}}{2 y} \]	✓	✓	✓

15738	\[ {} y^{\prime } = -\frac {3 x^{2}}{2 y} \]	✓	✓	✓

15739	\[ {} y^{\prime } = \frac {\sqrt {y}}{x} \]	✓	✓	✗

15740	\[ {} y^{\prime } = \frac {\sqrt {y}}{x} \]	✓	✓	✓

15741	\[ {} y^{\prime } = \frac {\sqrt {y}}{x} \]	✓	✓	✗

15742	\[ {} y^{\prime } = \frac {\sqrt {y}}{x} \]	✓	✓	✗

15743	\[ {} y^{\prime } = 3 x y^{{1}/{3}} \]	✓	✓	✗

15744	\[ {} y^{\prime } = 3 x y^{{1}/{3}} \]	✓	✓	✗

15745	\[ {} y^{\prime } = 3 x y^{{1}/{3}} \]	✓	✓	✗

15746	\[ {} y^{\prime } = 3 x y^{{1}/{3}} \]	✓	✓	✓

15747	\[ {} y^{\prime } = 3 x y^{{1}/{3}} \]	✓	✓	✗

15748	\[ {} y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]	✓	✓	✗

15749	\[ {} y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]	✓	✓	✓

15750	\[ {} y^{\prime } = \sqrt {\left (y+2\right ) \left (y-1\right )} \]	✓	✓	✗

15751	\[ {} y^{\prime } = \frac {y}{y-x} \]	✓	✓	✓

15752	\[ {} y^{\prime } = \frac {y}{y-x} \]	✓	✓	✓

15753	\[ {} y^{\prime } = \frac {y}{y-x} \]	✓	✓	✓

15754	\[ {} y^{\prime } = \frac {y}{y-x} \]	✓	✓	✓

15755	\[ {} y^{\prime } = \frac {x y}{x^{2}+y^{2}} \]	✓	✓	✓

15756	\[ {} y^{\prime } = \frac {x y}{x^{2}+y^{2}} \]	✓	✓	✗

15757	\[ {} y^{\prime } = \frac {x y}{x^{2}+y^{2}} \]	✓	✓	✓

15758	\[ {} y^{\prime } = x \sqrt {1-y^{2}} \]	✓	✓	✓

15759	\[ {} y^{\prime } = x \sqrt {1-y^{2}} \]	✓	✓	✗

15760	\[ {} y^{\prime } = x \sqrt {1-y^{2}} \]	✓	✓	✗

15761	\[ {} y^{\prime } = x \sqrt {1-y^{2}} \]	✓	✓	✗

15762	\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]	✓	✓	✗

15763	\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]	✓	✓	✓

15764	\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]	✓	✓	✗

15765	\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]	✓	✓	✗

15766	\[ {} y^{\prime } = -\frac {x}{2}+\frac {\sqrt {x^{2}+4 y}}{2} \]	✓	✓	✓

15796	\[ {} y^{\prime }-i y = 0 \]	✓	✓	✓

15808	\[ {} y^{\prime }-y = 0 \]	✓	✓	✓

15810	\[ {} 2 y+y^{\prime } = 4 \]	✓	✓	✓

15815	\[ {} y^{\prime } = {\mathrm e}^{x} \]	✓	✓	✓

15816	\[ {} y^{\prime }-y = 2 \,{\mathrm e}^{x} \]	✓	✓	✓

15822	\[ {} y^{\prime }-2 y = 6 \]	✓	✓	✓

15823	\[ {} y^{\prime }+y = {\mathrm e}^{x} \]	✓	✓	✓

15830	\[ {} 2 y+y^{\prime } = \left \{\begin {array}{cc} 2 & 0\le x <1 \\ 1 & 1\le x \end {array}\right . \]	✓	✓	✗

15837	\[ {} y^{\prime }+3 y = \delta \left (x -2\right ) \]	✓	✓	✓

15838	\[ {} y^{\prime }-3 y = \delta \left (x -1\right )+2 \operatorname {Heaviside}\left (x -2\right ) \]	✓	✓	✓

15888	\[ {} y^{\prime } = \frac {y+1}{t +1} \]	✓	✓	✓

15889	\[ {} y^{\prime } = t^{2} y^{2} \]	✓	✓	✓

15890	\[ {} y^{\prime } = t^{4} y \]	✓	✓	✓

15891	\[ {} y^{\prime } = 2 y+1 \]	✓	✓	✓

15892	\[ {} y^{\prime } = 2-y \]	✓	✓	✓

4.9.57 Problems 5601 to 5700