Internal problem ID [5332]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 5. Existence and uniqueness of solutions to first order equations. Page
198
Problem number: 1(g).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {2 \,{\mathrm e}^{2 x} y+2 \cos \relax (y) x +\left ({\mathrm e}^{2 x}-x^{2} \sin \relax (y)\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 19
dsolve((2*y(x)*exp(2*x)+2*x*cos(y(x)))+(exp(2*x)-x^2*sin(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
\[ \cos \left (y \relax (x )\right ) x^{2}+y \relax (x ) {\mathrm e}^{2 x}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.451 (sec). Leaf size: 30
DSolve[(2*y[x]*Exp[2*x]+2*x*Cos[y[x]])+(Exp[2*x]-x^2*Sin[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [2 \left (\frac {1}{2} x^2 \cos (y(x))+\frac {1}{2} e^{2 x} y(x)\right )=c_1,y(x)\right ] \]