49.22.7 problem 1(g)

Internal problem ID [7753]
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)
Date solved : Monday, January 27, 2025 at 03:12:04 PM
CAS classification : [_exact]

\begin{align*} 2 y \,{\mathrm e}^{2 x}+2 x \cos \left (y\right )+\left ({\mathrm e}^{2 x}-x^{2} \sin \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (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)
 

\[ y \,{\mathrm e}^{2 x}+\cos \left (y\right ) x^{2}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.423 (sec). Leaf size: 30

DSolve[(2*y[x]*Exp[2*x]+2*x*Cos[y[x]])+(Exp[2*x]-x^2*Sin[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [2 \left (\frac {1}{2} x^2 \cos (y(x))+\frac {1}{2} e^{2 x} y(x)\right )=c_1,y(x)\right ] \]