Internal problem ID [10338]
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]
\[ \boxed {g \left (x \right ) y^{\prime }-f_{1} \left (x \right ) y=f_{0} \left (x \right )} \]
✓ 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)
\[ y \left (x \right ) = \left (\int \frac {f_{0} \left (x \right ) {\mathrm e}^{-\left (\int \frac {f_{1} \left (x \right )}{g \left (x \right )}d x \right )}}{g \left (x \right )}d x +c_{1} \right ) {\mathrm e}^{\int \frac {f_{1} \left (x \right )}{g \left (x \right )}d x} \]
✓ Solution by Mathematica
Time used: 0.135 (sec). Leaf size: 64
DSolve[g[x]*y'[x]==f1[x]*y[x]+f0[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \exp \left (\int _1^x\frac {\text {f1}(K[1])}{g(K[1])}dK[1]\right ) \left (\int _1^x\frac {\exp \left (-\int _1^{K[2]}\frac {\text {f1}(K[1])}{g(K[1])}dK[1]\right ) \text {f0}(K[2])}{g(K[2])}dK[2]+c_1\right ) \]