Internal problem ID [8704]
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`]]
\[ \boxed {{y^{\prime }}^{2}+a y=-x^{2} b} \]
✗ 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: 1.1 (sec). Leaf size: 581
DSolve[b*x^2 + a*y[x] + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^4-\text {$\#$1}^3 a+2 \text {$\#$1}^2 b+\text {$\#$1} a b+b^2\&,\frac {2 \text {$\#$1}^3 \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )-2 \text {$\#$1}^3 \log (x)-\text {$\#$1}^2 a \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+\text {$\#$1}^2 a \log (x)+2 \text {$\#$1} b \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+a b \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )-2 \text {$\#$1} b \log (x)-a b \log (x)}{4 \text {$\#$1}^3-3 \text {$\#$1}^2 a+4 \text {$\#$1} b+a b}\&\right ]-\log \left (\sqrt {-a y(x)} \sqrt {-a y(x)-b x^2}+a y(x)\right )+\frac {1}{2} \log (y(x))+2 \log (x)&=c_1,y(x)\right ] \\ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^4+\text {$\#$1}^3 a+2 \text {$\#$1}^2 b-\text {$\#$1} a b+b^2\&,\frac {-2 \text {$\#$1}^3 \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+2 \text {$\#$1}^3 \log (x)-\text {$\#$1}^2 a \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+\text {$\#$1}^2 a \log (x)-2 \text {$\#$1} b \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+a b \log \left (\text {$\#$1} x-\sqrt {-a y(x)-b x^2}+\sqrt {-a y(x)}\right )+2 \text {$\#$1} b \log (x)-a b \log (x)}{-4 \text {$\#$1}^3-3 \text {$\#$1}^2 a-4 \text {$\#$1} b+a b}\&\right ]-\log \left (\sqrt {-a y(x)} \sqrt {-a y(x)-b x^2}+a y(x)\right )+\frac {1}{2} \log (y(x))+2 \log (x)&=c_1,y(x)\right ] \\ \end{align*}