78.8.40 problem 40

Internal problem ID [18238]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 11:43:18 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 20

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

\[ x^{3} {\mathrm e}^{y}-x^{2}+\cos \left (y\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.274 (sec). Leaf size: 23

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

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