Problems 301 to 400

Table 4.1129: First order ode non-linear in derivative


#	ODE	Mathematica	Maple	Sympy

5578	\[ {} y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x +x^{2} = 0 \]	✓	✓	✓

5579	\[ {} y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x +a -y^{2} = 0 \]	✓	✓	✗

5580	\[ {} y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+2 y^{2} = 0 \]	✓	✓	✗

5581	\[ {} y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x +a -x^{2}+2 y^{2} = 0 \]	✓	✓	✗

5582	\[ {} y^{2} {y^{\prime }}^{2}+2 a x y y^{\prime }+\left (a -1\right ) b +x^{2} a +\left (1-a \right ) y^{2} = 0 \]	✓	✓	✗

5583	\[ {} \left (1-y^{2}\right ) {y^{\prime }}^{2} = 1 \]	✓	✓	✓

5584	\[ {} \left (a^{2}-y^{2}\right ) {y^{\prime }}^{2} = y^{2} \]	✓	✓	✓

5585	\[ {} \left (a^{2}-2 a x y+y^{2}\right ) {y^{\prime }}^{2}+2 a y y^{\prime }+y^{2} = 0 \]	✗	✗	✗

5586	\[ {} \left (a^{2} x^{2}-y^{2}\right ) {y^{\prime }}^{2}-2 y y^{\prime } x +x^{2} \left (a^{2}-1\right ) = 0 \]	✓	✓	✗

5587	\[ {} \left (\left (1-a \right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a x y y^{\prime }+x^{2}+\left (1-a \right ) y^{2} = 0 \]	✓	✓	✗

5588	\[ {} \left (\left (-4 a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}-8 a^{2} x y y^{\prime }+x^{2}+\left (-4 a^{2}+1\right ) y^{2} = 0 \]	✓	✓	✓

5589	\[ {} \left (\left (-a^{2}+1\right ) x^{2}+y^{2}\right ) {y^{\prime }}^{2}+2 a^{2} x y y^{\prime }+x^{2}+\left (-a^{2}+1\right ) y^{2} = 0 \]	✓	✓	✗

5590	\[ {} \left (x +y\right )^{2} {y^{\prime }}^{2} = y^{2} \]	✓	✓	✓

5591	\[ {} \left (x +y\right )^{2} {y^{\prime }}^{2}-\left (x^{2}-x y-2 y^{2}\right ) y^{\prime }-\left (x -y\right ) y = 0 \]	✓	✓	✓

5592	\[ {} \left (a^{2}-\left (x -y\right )^{2}\right ) {y^{\prime }}^{2}+2 a^{2} y^{\prime }+a^{2}-\left (x -y\right )^{2} = 0 \]	✓	✓	✓

5593	\[ {} 2 y^{2} {y^{\prime }}^{2}+2 y y^{\prime } x -1+x^{2}+y^{2} = 0 \]	✓	✓	✗

5594	\[ {} 3 y^{2} {y^{\prime }}^{2}-2 y y^{\prime } x -x^{2}+4 y^{2} = 0 \]	✓	✓	✓

5595	\[ {} 4 y^{2} {y^{\prime }}^{2}+2 \left (3 x +1\right ) x y y^{\prime }+3 x^{3} = 0 \]	✓	✓	✓

5596	\[ {} \left (x^{2}-4 y^{2}\right ) {y^{\prime }}^{2}+6 y y^{\prime } x -4 x^{2}+y^{2} = 0 \]	✓	✓	✗

5597	\[ {} 9 y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y = 0 \]	✓	✓	✗

5598	\[ {} \left (2-3 y\right )^{2} {y^{\prime }}^{2} = 4-4 y \]	✓	✓	✓

5599	\[ {} \left (-a^{2}+1\right ) y^{2} {y^{\prime }}^{2}-3 a^{2} x y y^{\prime }-a^{2} x^{2}+y^{2} = 0 \]	✓	✓	✗

5600	\[ {} \left (a -b \right ) y^{2} {y^{\prime }}^{2}-2 b x y y^{\prime }-a b -b \,x^{2}+a y^{2} = 0 \]	✓	✓	✗

5601	\[ {} a^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) {y^{\prime }}^{2}+2 a \,b^{2} c y^{\prime }+c^{2} \left (b^{2}-\left (c x -a y\right )^{2}\right ) = 0 \]	✓	✓	✗

5602	\[ {} x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }+a^{2} x = 0 \]	✓	✓	✗

5603	\[ {} x y^{2} {y^{\prime }}^{2}+\left (a -x^{3}-y^{3}\right ) y^{\prime }+x^{2} y = 0 \]	✓	✓	✗

5604	\[ {} 2 x y^{2} {y^{\prime }}^{2}-y^{3} y^{\prime }-a = 0 \]	✓	✓	✗

5605	\[ {} 4 y^{2} {y^{\prime }}^{2} x^{2} = \left (x^{2}+y^{2}\right )^{2} \]	✓	✓	✓

5606	\[ {} 4 y^{3} {y^{\prime }}^{2}-4 x y^{\prime }+y = 0 \]	✓	✓	✗

5607	\[ {} 3 x y^{4} {y^{\prime }}^{2}-y^{5} y^{\prime }+1 = 0 \]	✓	✓	✗

5608	\[ {} 9 x y^{4} {y^{\prime }}^{2}-3 y^{5} y^{\prime }-a = 0 \]	✓	✓	✗

5609	\[ {} 9 \left (-x^{2}+1\right ) y^{4} {y^{\prime }}^{2}+6 x y^{5} y^{\prime }+4 x^{2} = 0 \]	✓	✓	✗

5610	\[ {} {y^{\prime }}^{3} = b x +a \]	✓	✓	✓

5611	\[ {} {y^{\prime }}^{3} = a \,x^{n} \]	✓	✓	✓

5612	\[ {} {y^{\prime }}^{3}+x -y = 0 \]	✓	✓	✓

5613	\[ {} {y^{\prime }}^{3} = \left (a +b y+c y^{2}\right ) f \left (x \right ) \]	✓	✓	✓

5614	\[ {} {y^{\prime }}^{3} = \left (y-a \right )^{2} \left (y-b \right )^{2} \]	✓	✓	✓

5615	\[ {} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} = 0 \]	✓	✓	✓

5616	\[ {} {y^{\prime }}^{3}+f \left (x \right ) \left (y-a \right )^{2} \left (y-b \right )^{2} \left (y-c \right )^{2} = 0 \]	✓	✓	✓

5617	\[ {} {y^{\prime }}^{3}+y^{\prime }+a -b x = 0 \]	✓	✓	✓

5618	\[ {} {y^{\prime }}^{3}+y^{\prime }-y = 0 \]	✓	✓	✓

5619	\[ {} {y^{\prime }}^{3}+y^{\prime } = {\mathrm e}^{y} \]	✓	✓	✗

5620	\[ {} {y^{\prime }}^{3}-7 y^{\prime }+6 = 0 \]	✓	✓	✓

5621	\[ {} {y^{\prime }}^{3}-x y^{\prime }+a y = 0 \]	✗	✓	✗

5622	\[ {} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \]	✗	✓	✗

5623	\[ {} {y^{\prime }}^{3}-2 x y^{\prime }-y = 0 \]	✗	✓	✗

5624	\[ {} {y^{\prime }}^{3}-a x y^{\prime }+x^{3} = 0 \]	✓	✓	✓

5625	\[ {} {y^{\prime }}^{3}+a x y^{\prime }-a y = 0 \]	✓	✓	✗

5626	\[ {} {y^{\prime }}^{3}-\left (b x +a \right ) y^{\prime }+b y = 0 \]	✓	✓	✗

5627	\[ {} {y^{\prime }}^{3}-2 y y^{\prime }+y^{2} = 0 \]	✓	✓	✓

5628	\[ {} {y^{\prime }}^{3}-a x y y^{\prime }+2 a y^{2} = 0 \]	✓	✓	✗

5629	\[ {} {y^{\prime }}^{3}-y^{4} y^{\prime } x -y^{5} = 0 \]	✓	✓	✗

5630	\[ {} {y^{\prime }}^{3}+{\mathrm e}^{3 x -2 y} \left (y^{\prime }-1\right ) = 0 \]	✗	✓	✗

5631	\[ {} {y^{\prime }}^{3}+{\mathrm e}^{-2 y} \left ({\mathrm e}^{2 x}+{\mathrm e}^{3 x}\right ) y^{\prime }-{\mathrm e}^{3 x -2 y} = 0 \]	✗	✓	✗

5632	\[ {} {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0 \]	✓	✓	✓

5633	\[ {} {y^{\prime }}^{3}-{y^{\prime }}^{2}+y^{2} = 0 \]	✓	✓	✓

5634	\[ {} {y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y = 0 \]	✓	✓	✗

5635	\[ {} {y^{\prime }}^{3}-a {y^{\prime }}^{2}+b y+a b x = 0 \]	✓	✓	✗

5636	\[ {} {y^{\prime }}^{3}+a_{0} {y^{\prime }}^{2}+a_{1} y^{\prime }+a_{2} +a_{3} y = 0 \]	✗	✓	✗

5637	\[ {} {y^{\prime }}^{3}+\left (1-3 x \right ) {y^{\prime }}^{2}-x \left (1-3 x \right ) y^{\prime }-1-x^{3} = 0 \]	✓	✓	✓

5638	\[ {} {y^{\prime }}^{3}-y {y^{\prime }}^{2}+y^{2} = 0 \]	✓	✓	✓

5639	\[ {} {y^{\prime }}^{3}+\left (\cos \left (x \right ) \cot \left (x \right )-y\right ) {y^{\prime }}^{2}-\left (1+y \cos \left (x \right ) \cot \left (x \right )\right ) y^{\prime }+y = 0 \]	✓	✓	✓

5640	\[ {} {y^{\prime }}^{3}+\left (2 x -y^{2}\right ) {y^{\prime }}^{2}-2 x y^{2} y^{\prime } = 0 \]	✓	✓	✓

5641	\[ {} {y^{\prime }}^{3}-\left (y^{2}+2 x \right ) {y^{\prime }}^{2}+\left (x^{2}-y^{2}+2 x y^{2}\right ) y^{\prime }-\left (x^{2}-y^{2}\right ) y^{2} = 0 \]	✓	✓	✓

5642	\[ {} {y^{\prime }}^{3}-\left (x^{2}+x y+y^{2}\right ) {y^{\prime }}^{2}+x y \left (x^{2}+x y+y^{2}\right ) y^{\prime }-x^{3} y^{3} = 0 \]	✓	✓	✓

5643	\[ {} {y^{\prime }}^{3}-\left (x^{2}+x y^{2}+y^{4}\right ) {y^{\prime }}^{2}+x y^{2} \left (x^{2}+x y^{2}+y^{4}\right ) y^{\prime }-x^{3} y^{6} = 0 \]	✓	✓	✓

5644	\[ {} 2 {y^{\prime }}^{3}+x y^{\prime }-2 y = 0 \]	✗	✓	✗

5645	\[ {} 2 {y^{\prime }}^{3}+{y^{\prime }}^{2}-y = 0 \]	✗	✓	✓

5646	\[ {} 3 {y^{\prime }}^{3}-x^{4} y^{\prime }+2 x^{3} y = 0 \]	✓	✓	✗

5647	\[ {} 4 {y^{\prime }}^{3}+4 y^{\prime } = x \]	✓	✓	✓

5648	\[ {} 8 {y^{\prime }}^{3}+12 {y^{\prime }}^{2} = 27 x +27 y \]	✗	✓	✗

5649	\[ {} x {y^{\prime }}^{3}-y {y^{\prime }}^{2}+a = 0 \]	✓	✓	✗

5650	\[ {} x {y^{\prime }}^{3}-\left (x +x^{2}+y\right ) {y^{\prime }}^{2}+\left (x^{2}+y+x y\right ) y^{\prime }-x y = 0 \]	✓	✓	✓

5651	\[ {} x {y^{\prime }}^{3}-2 y {y^{\prime }}^{2}+4 x^{2} = 0 \]	✓	✓	✗

5652	\[ {} 2 x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2}-x = 0 \]	✓	✓	✗

5653	\[ {} 4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}-x +3 y = 0 \]	✓	✓	✗

5654	\[ {} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y = 0 \]	✓	✓	✗

5655	\[ {} x^{2} {y^{\prime }}^{3}-2 x y {y^{\prime }}^{2}+y^{2} y^{\prime }+1 = 0 \]	✓	✓	✗

5656	\[ {} \left (a^{2}-x^{2}\right ) {y^{\prime }}^{3}+b x \left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}-y^{\prime }-b x = 0 \]	✓	✓	✓

5657	\[ {} x {y^{\prime }}^{3}-3 y {y^{\prime }}^{2} x^{2}+x \left (x^{5}+3 y^{2}\right ) y^{\prime }-2 x^{5} y-y^{3} = 0 \]	✗	✗	✗

5658	\[ {} 2 {y^{\prime }}^{3} x^{3}+6 y {y^{\prime }}^{2} x^{2}-\left (1-6 x y\right ) y y^{\prime }+2 y^{3} = 0 \]	✓	✓	✗

5659	\[ {} {y^{\prime }}^{3} x^{4}-y {y^{\prime }}^{2} x^{3}-x^{2} y^{2} y^{\prime }+x y^{3} = 1 \]	✓	✓	✗

5660	\[ {} x^{6} {y^{\prime }}^{3}-x y^{\prime }-y = 0 \]	✗	✓	✗

5661	\[ {} {y^{\prime }}^{3} y-3 x y^{\prime }+3 y = 0 \]	✓	✓	✓

5662	\[ {} 2 {y^{\prime }}^{3} y-3 x y^{\prime }+2 y = 0 \]	✓	✓	✗

5663	\[ {} \left (2 y+x \right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+\left (y+2 x \right ) y^{\prime } = 0 \]	✓	✓	✓

5664	\[ {} y^{2} {y^{\prime }}^{3}-x y^{\prime }+y = 0 \]	✗	✓	✗

5665	\[ {} y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \]	✓	✓	✗

5666	\[ {} 4 y^{2} {y^{\prime }}^{3}-2 x y^{\prime }+y = 0 \]	✓	✓	✗

5667	\[ {} 16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y = 0 \]	✓	✓	✗

5668	\[ {} x y^{2} {y^{\prime }}^{3}-y^{3} {y^{\prime }}^{2}+x \left (x^{2}+1\right ) y^{\prime }-x^{2} y = 0 \]	✓	✗	✗

5669	\[ {} y^{3} {y^{\prime }}^{3}-\left (1-3 x \right ) y^{2} {y^{\prime }}^{2}+3 x^{2} y y^{\prime }+x^{3}-y^{2} = 0 \]	✗	✓	✗

5670	\[ {} y^{4} {y^{\prime }}^{3}-6 x y^{\prime }+2 y = 0 \]	✓	✓	✗

5671	\[ {} {y^{\prime }}^{4} = \left (y-a \right )^{3} \left (y-b \right )^{2} \]	✓	✓	✓

5672	\[ {} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{2} = 0 \]	✓	✓	✓

5673	\[ {} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} = 0 \]	✓	✓	✓

5674	\[ {} {y^{\prime }}^{4}+f \left (x \right ) \left (y-a \right )^{3} \left (y-b \right )^{3} \left (y-c \right )^{2} = 0 \]	✓	✓	✓

5675	\[ {} {y^{\prime }}^{4}+x y^{\prime }-3 y = 0 \]	✗	✓	✗

5676	\[ {} {y^{\prime }}^{4}-4 y {y^{\prime }}^{2} x^{2}+16 x y^{2} y^{\prime }-16 y^{3} = 0 \]	✓	✓	✗

5677	\[ {} {y^{\prime }}^{4}+4 {y^{\prime }}^{3} y+6 y^{2} {y^{\prime }}^{2}-\left (1-4 y^{3}\right ) y^{\prime }-\left (3-y^{3}\right ) y = 0 \]	✓	✓	✓

4.14.4 Problems 301 to 400