Internal problem ID [3396]
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`]]
\[ \boxed {2 y^{\prime }-\sqrt {a^{2} x^{2}-4 b \,x^{2}-4 c y}=-a x} \]
✓ Solution by Maple
Time used: 0.047 (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)
\[ \int _{\textit {\_b}}^{x}-\frac {-a \textit {\_a} +\sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 c y \left (x \right )}}{-a \,\textit {\_a}^{2}+\textit {\_a} \sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 c y \left (x \right )}-4 y \left (x \right )}d \textit {\_a} +\int _{}^{y \left (x \right )}\left (\frac {2}{-a \,x^{2}+x \sqrt {a^{2} x^{2}-4 b \,x^{2}-4 \textit {\_f} c}-4 \textit {\_f}}-\left (\int _{\textit {\_b}}^{x}\left (\frac {2 c}{\sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}\, \left (-a \,\textit {\_a}^{2}+\textit {\_a} \sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}-4 \textit {\_f} \right )}+\frac {\left (-a \textit {\_a} +\sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}\right ) \left (-\frac {2 \textit {\_a} c}{\sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}}-4\right )}{\left (-a \,\textit {\_a}^{2}+\textit {\_a} \sqrt {\textit {\_a}^{2} a^{2}-4 \textit {\_a}^{2} b -4 \textit {\_f} c}-4 \textit {\_f} \right )^{2}}\right )d \textit {\_a} \right )\right )d \textit {\_f} +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.586 (sec). Leaf size: 542
DSolve[2 y'[x]+a x==Sqrt[a^2 x^2-4 b x^2 -4 c y[x]],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^4+2 \text {$\#$1}^3 c-2 \text {$\#$1}^2 a^2-4 \text {$\#$1}^2 a c+8 \text {$\#$1}^2 b+2 \text {$\#$1} a^2 c-8 \text {$\#$1} b c+a^4-8 a^2 b+16 b^2\&,\frac {\text {$\#$1}^3 \log \left (\text {$\#$1} x-\sqrt {x^2 \left (a^2-4 b\right )-4 c y(x)}+2 \sqrt {-c y(x)}\right )+\text {$\#$1}^3 (-\log (x))+\text {$\#$1}^2 c \log \left (\text {$\#$1} x-\sqrt {x^2 \left (a^2-4 b\right )-4 c y(x)}+2 \sqrt {-c y(x)}\right )-\text {$\#$1}^2 c \log (x)-\text {$\#$1} a^2 \log \left (\text {$\#$1} x-\sqrt {x^2 \left (a^2-4 b\right )-4 c y(x)}+2 \sqrt {-c y(x)}\right )+4 \text {$\#$1} b \log \left (\text {$\#$1} x-\sqrt {x^2 \left (a^2-4 b\right )-4 c y(x)}+2 \sqrt {-c y(x)}\right )-2 \text {$\#$1} a c \log \left (\text {$\#$1} x-\sqrt {x^2 \left (a^2-4 b\right )-4 c y(x)}+2 \sqrt {-c y(x)}\right )+a^2 c \log \left (\text {$\#$1} x-\sqrt {x^2 \left (a^2-4 b\right )-4 c y(x)}+2 \sqrt {-c y(x)}\right )-4 b c \log \left (\text {$\#$1} x-\sqrt {x^2 \left (a^2-4 b\right )-4 c y(x)}+2 \sqrt {-c y(x)}\right )+\text {$\#$1} a^2 \log (x)+2 \text {$\#$1} a c \log (x)-4 \text {$\#$1} b \log (x)-a^2 c \log (x)+4 b c \log (x)}{2 \text {$\#$1}^3+3 \text {$\#$1}^2 c-2 \text {$\#$1} a^2-4 \text {$\#$1} a c+8 \text {$\#$1} b+a^2 c-4 b c}\&\right ]-\log \left (\sqrt {-c y(x)} \sqrt {x^2 \left (a^2-4 b\right )-4 c y(x)}+2 c y(x)\right )+\frac {1}{2} \log (y(x))+2 \log (x)=c_1,y(x)\right ] \]