20.4.46 problem Problem 64

Internal problem ID [3681]
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
Date solved : Monday, January 27, 2025 at 07:54:42 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} \frac {y^{\prime }}{y}+p \left (x \right ) \ln \left (y\right )&=q \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.242 (sec). Leaf size: 27

dsolve(diff(y(x),x)/y(x)+p(x)*ln(y(x))=q(x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{{\mathrm e}^{-\int p \left (x \right )d x} \left (\int q \left (x \right ) {\mathrm e}^{\int p \left (x \right )d x}d x -c_{1} \right )} \]

✓ Solution by Mathematica

Time used: 0.195 (sec). Leaf size: 109

DSolve[D[y[x],x]/y[x]+p[x]*Log[y[x]]==q[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^x\exp \left (-\int _1^{K[2]}-p(K[1])dK[1]\right ) (\log (y(x)) p(K[2])-q(K[2]))dK[2]+\int _1^{y(x)}\left (\frac {\exp \left (-\int _1^x-p(K[1])dK[1]\right )}{K[3]}-\int _1^x\frac {\exp \left (-\int _1^{K[2]}-p(K[1])dK[1]\right ) p(K[2])}{K[3]}dK[2]\right )dK[3]=c_1,y(x)\right ] \]