Internal problem ID [3497]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 9
Problem number: 241.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 x y^{\prime }+4 y+\sqrt {a^{2}-4 b -4 c y}=-a} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(2*x*diff(y(x),x)+4*y(x)+a+sqrt(a^2-4*b-4*c*y(x)) = 0,y(x), singsol=all)
\[ \ln \left (x \right )+\int _{}^{y \left (x \right )}-\frac {1}{-2 \textit {\_a} -\frac {a}{2}-\frac {\sqrt {-4 \textit {\_a} c +a^{2}-4 b}}{2}}d \textit {\_a} +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.808 (sec). Leaf size: 177
DSolve[2 x y'[x]+4 y[x]+a +Sqrt[a^2-4 b- 4 c y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{4} \left (\log \left (c \left (\sqrt {a^2-4 (\text {$\#$1} c+b)}+4 \text {$\#$1}+a\right )\right )-\frac {2 c \arctan \left (\frac {c-2 \sqrt {a^2-4 (\text {$\#$1} c+b)}}{\sqrt {-4 a^2-4 a c+16 b-c^2}}\right )}{\sqrt {-4 a^2-4 a c+16 b-c^2}}\right )\&\right ]\left [-\frac {\log (x)}{2}+c_1\right ] y(x)\to \frac {1}{8} \left (-\sqrt {(2 a+c)^2-16 b}-2 a-c\right ) y(x)\to \frac {1}{8} \left (\sqrt {(2 a+c)^2-16 b}-2 a-c\right ) \end{align*}