Internal problem ID [7948]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 368.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+a y+x^{2} b=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(y(x),x)^2+a*y(x)+b*x^2 = 0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 14.485 (sec). Leaf size: 795
DSolve[b*x^2 + a*y[x] + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\int _1^{y(x)}\left (-\frac {\sqrt {-b x^2-a K[2]} x}{b x^4+a K[2] x^2+4 K[2]^2}-\int _1^x\left (\frac {a K[1]}{b K[1]^4+a K[2] K[1]^2+4 K[2]^2}+\frac {2 \sqrt {-b K[1]^2-a K[2]}}{b K[1]^4+a K[2] K[1]^2+4 K[2]^2}-\frac {a K[2]}{\sqrt {-b K[1]^2-a K[2]} \left (b K[1]^4+a K[2] K[1]^2+4 K[2]^2\right )}-\frac {\left (a K[1]^2+8 K[2]\right ) \left (b K[1]^3+a K[2] K[1]\right )}{\left (b K[1]^4+a K[2] K[1]^2+4 K[2]^2\right )^2}-\frac {2 K[2] \left (a K[1]^2+8 K[2]\right ) \sqrt {-b K[1]^2-a K[2]}}{\left (b K[1]^4+a K[2] K[1]^2+4 K[2]^2\right )^2}\right )dK[1]+\frac {2 K[2]}{b x^4+a K[2] x^2+4 K[2]^2}\right )dK[2]+\int _1^x\left (\frac {2 \sqrt {-b K[1]^2-a y(x)} y(x)}{b K[1]^4+a y(x) K[1]^2+4 y(x)^2}+\frac {b K[1]^3+a y(x) K[1]}{b K[1]^4+a y(x) K[1]^2+4 y(x)^2}\right )dK[1]=c_1,y(x)\right ] \\ \text {Solve}\left [\int _1^{y(x)}\left (\frac {\sqrt {-b x^2-a K[4]} x}{b x^4+a K[4] x^2+4 K[4]^2}-\int _1^x\left (\frac {a K[3]}{b K[3]^4+a K[4] K[3]^2+4 K[4]^2}-\frac {2 \sqrt {-b K[3]^2-a K[4]}}{b K[3]^4+a K[4] K[3]^2+4 K[4]^2}+\frac {a K[4]}{\sqrt {-b K[3]^2-a K[4]} \left (b K[3]^4+a K[4] K[3]^2+4 K[4]^2\right )}-\frac {\left (a K[3]^2+8 K[4]\right ) \left (b K[3]^3+a K[4] K[3]\right )}{\left (b K[3]^4+a K[4] K[3]^2+4 K[4]^2\right )^2}+\frac {2 K[4] \left (a K[3]^2+8 K[4]\right ) \sqrt {-b K[3]^2-a K[4]}}{\left (b K[3]^4+a K[4] K[3]^2+4 K[4]^2\right )^2}\right )dK[3]+\frac {2 K[4]}{b x^4+a K[4] x^2+4 K[4]^2}\right )dK[4]+\int _1^x\left (\frac {b K[3]^3+a y(x) K[3]}{b K[3]^4+a y(x) K[3]^2+4 y(x)^2}-\frac {2 y(x) \sqrt {-b K[3]^2-a y(x)}}{b K[3]^4+a y(x) K[3]^2+4 y(x)^2}\right )dK[3]=c_1,y(x)\right ] \\ \end{align*}