Internal problem ID [2888]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 5
Problem number: 140.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {2 y^{\prime }+a x -\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 269
dsolve(2*diff(y(x),x)+a*x = sqrt(a^2*x^2-4*b*x^2-4*c*y(x)),y(x), singsol=all)
\[ \int _{\textit {\_b}}^{x}-\frac {-a \textit {\_a} +\sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 c y \relax (x )}}{-a \,\textit {\_a}^{2}+\textit {\_a} \sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 c y \relax (x )}-4 y \relax (x )}d \textit {\_a} +\int _{}^{y \relax (x )}\left (\frac {2}{-a \,x^{2}+x \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 \textit {\_f} c}-4 \textit {\_f}}-\left (\int _{\textit {\_b}}^{x}\left (\frac {2 c}{\sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}\, \left (-a \,\textit {\_a}^{2}+\textit {\_a} \sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}-4 \textit {\_f} \right )}+\frac {\left (-a \textit {\_a} +\sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}\right ) \left (-\frac {2 \textit {\_a} c}{\sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}}-4\right )}{\left (-a \,\textit {\_a}^{2}+\textit {\_a} \sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}-4 \textit {\_f} \right )^{2}}\right )d \textit {\_a} \right )\right )d \textit {\_f} +c_{1} = 0 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[2 y'[x]+a x==Sqrt[a^2 x^2-4 b x^2 -4 c y[x]],y[x],x,IncludeSingularSolutions -> True]
Timed out