Internal problem ID [926]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 48(c).
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 {x y^{\prime }}{y}+2 \ln \relax (y)-4 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x)/y(x)+2*ln(y(x))= 4*x^2,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x^{2}} {\mathrm e}^{-\frac {c_{1}}{x^{2}}} \]
✓ Solution by Mathematica
Time used: 0.224 (sec). Leaf size: 17
DSolve[x*y'[x]/y[x]+2*Log[y[x]]== 4*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{x^2+\frac {c_1}{x^2}} \\ \end{align*}