7.5.57 problem 57

Internal problem ID [161]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 57
Date solved : Friday, February 07, 2025 at 07:59:11 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

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

✓ Solution by Maple

Time used: 0.204 (sec). Leaf size: 27

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

\[ y = {\mathrm e}^{{\mathrm e}^{\int q \left (x \right )d x} \left (-\int p \left (x \right ) {\mathrm e}^{-\int q \left (x \right )d x}d x +c_1 \right )} \]

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 104

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

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