8.6.4 problem 4

Internal problem ID [774]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Chapter 1 review problems. Page 78
Problem number : 4
Date solved : Monday, January 27, 2025 at 03:04:41 AM
CAS classification : [_exact]

\begin{align*} 2 x y^{3}+{\mathrm e}^{x}+\left (3 x^{2} y^{2}+\sin \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.017 (sec). Leaf size: 20

dsolve(exp(x)+2*x*y(x)^3+(sin(y(x))+3*x^2*y(x)^2)*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ x^{2} y^{3}+{\mathrm e}^{x}-\cos \left (y\right )+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.250 (sec). Leaf size: 23

DSolve[Exp[x]+2*x*y[x]^3+(Sin[y[x]]+3*x^2*y[x]^2)*D[y[x],x]== 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x^2 y(x)^3-\cos (y(x))+e^x=c_1,y(x)\right ] \]