Internal problem ID [3995]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 26
Problem number: 754.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class G`]]
\[ \boxed {{y^{\prime }}^{2}+y b=-x^{2} a} \]
✗ Solution by Maple
dsolve(diff(y(x),x)^2+a*x^2+b*y(x) = 0,y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 1.739 (sec). Leaf size: 581
DSolve[(y'[x])^2+a x^2+b y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^4-\text {$\#$1}^3 b+2 \text {$\#$1}^2 a+\text {$\#$1} a b+a^2\&,\frac {2 \text {$\#$1}^3 \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )-2 \text {$\#$1}^3 \log (x)-\text {$\#$1}^2 b \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+\text {$\#$1}^2 b \log (x)+2 \text {$\#$1} a \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+a b \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )-2 \text {$\#$1} a \log (x)-a b \log (x)}{4 \text {$\#$1}^3-3 \text {$\#$1}^2 b+4 \text {$\#$1} a+a b}\&\right ]-\log \left (\sqrt {-b y(x)} \sqrt {-a x^2-b y(x)}+b y(x)\right )+\frac {1}{2} \log (y(x))+2 \log (x)&=c_1,y(x)\right ] \\ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^4+\text {$\#$1}^3 b+2 \text {$\#$1}^2 a-\text {$\#$1} a b+a^2\&,\frac {-2 \text {$\#$1}^3 \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+2 \text {$\#$1}^3 \log (x)-\text {$\#$1}^2 b \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+\text {$\#$1}^2 b \log (x)-2 \text {$\#$1} a \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+a b \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+2 \text {$\#$1} a \log (x)-a b \log (x)}{-4 \text {$\#$1}^3-3 \text {$\#$1}^2 b-4 \text {$\#$1} a+a b}\&\right ]-\log \left (\sqrt {-b y(x)} \sqrt {-a x^2-b y(x)}+b y(x)\right )+\frac {1}{2} \log (y(x))+2 \log (x)&=c_1,y(x)\right ] \\ \end{align*}