7.5.58 problem 58

Internal problem ID [162]
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 : 58
Date solved : Friday, February 07, 2025 at 07:59:13 AM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]

\begin{align*} x y^{\prime }-4 y x^{2}+2 \ln \left (y\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 14

dsolve(x*diff(y(x),x)-4*x^2*y(x)+2*y(x)*ln(y(x))=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{\frac {x^{4}+c_1}{x^{2}}} \]

✓ Solution by Mathematica

Time used: 0.221 (sec). Leaf size: 17

DSolve[x*D[y[x],x]-4*x^2*y[x]+2*y[x]*Log[ y[x] ]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x^2+\frac {c_1}{x^2}} \]