Internal problem ID [9585]
Book: Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second
edition
Section: Chapter 1, First-Order differential equations
Problem number: 1.1.4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {g \relax (x ) y^{\prime }-f_{1} \relax (x ) y-f_{0} \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 38
dsolve(g(x)*diff(y(x),x)=f__1(x)*y(x)+f__0(x),y(x), singsol=all)
\[ y \relax (x ) = \left (\int \frac {f_{0} \relax (x ) {\mathrm e}^{-\left (\int \frac {f_{1} \relax (x )}{g \relax (x )}d x \right )}}{g \relax (x )}d x +c_{1}\right ) {\mathrm e}^{\int \frac {f_{1} \relax (x )}{g \relax (x )}d x} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 64
DSolve[g[x]*y'[x]==f1[x]*y[x]+f0[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \exp \left (\int _1^x\frac {\text {f1}(K[1])}{g(K[1])}dK[1]\right ) \left (\int _1^x\frac {\exp \left (-\int _1^{K[2]}\frac {\text {f1}(K[1])}{g(K[1])}dK[1]\right ) \text {f0}(K[2])}{g(K[2])}dK[2]+c_1\right ) \\ \end{align*}