Internal problem ID [2201]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 64.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_1st_order, _with_symmetry_[F(x),G(x)*y+H(x)]]]
Solve \begin {gather*} \boxed {\frac {y^{\prime }}{y}+p \relax (x ) \ln \relax (y)-q \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 36
dsolve(diff(y(x),x)/y(x)+p(x)*ln(y(x))=q(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{{\mathrm e}^{\int -p \relax (x )d x} \left (\int q \relax (x ) {\mathrm e}^{\int p \relax (x )d x}d x \right )} {\mathrm e}^{-{\mathrm e}^{\int -p \relax (x )d x} c_{1}} \]
✓ Solution by Mathematica
Time used: 0.164 (sec). Leaf size: 109
DSolve[y'[x]/y[x]+p[x]*Log[y[x]]==q[x],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\int _1^x\exp \left (-\int _1^{K[2]}-p(K[1])dK[1]\right ) (\log (y(x)) p(K[2])-q(K[2]))dK[2]+\int _1^{y(x)}\left (\frac {\exp \left (-\int _1^x-p(K[1])dK[1]\right )}{K[3]}-\int _1^x\frac {\exp \left (-\int _1^{K[2]}-p(K[1])dK[1]\right ) p(K[2])}{K[3]}dK[2]\right )dK[3]=c_1,y(x)\right ] \]