Internal problem ID [2831]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 3
Problem number: 76.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (a +b y+y^{2} c \right ) f \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 60
dsolve(diff(y(x),x) = (a+b*y(x)+c*y(x)^2)*f(x),y(x), singsol=all)
\[ y \relax (x ) = -\frac {-\tan \left (\frac {\left (\int f \relax (x )d x \right ) \sqrt {4 a c -b^{2}}}{2}+\frac {c_{1} \sqrt {4 a c -b^{2}}}{2}\right ) \sqrt {4 a c -b^{2}}+b}{2 c} \]
✓ Solution by Mathematica
Time used: 0.264 (sec). Leaf size: 115
DSolve[y'[x]==(a+b y[x]+c y[x]^2)f[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-b+\sqrt {4 a c-b^2} \tan \left (\frac {1}{2} \sqrt {4 a c-b^2} \left (\int _1^xf(K[1])dK[1]+c_1\right )\right )}{2 c} \\ y(x)\to -\frac {\sqrt {b^2-4 a c}+b}{2 c} \\ y(x)\to \frac {\sqrt {b^2-4 a c}-b}{2 c} \\ \end{align*}