78.4.11 problem 12

Internal problem ID [18134]
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. Section 8 (Exact Equations). Problems at page 72
Problem number : 12
Date solved : Tuesday, January 28, 2025 at 11:31:32 AM
CAS classification : [_exact]

\begin{align*} 2 x y^{4}+\sin \left (y\right )+\left (4 x^{2} y^{3}+x \cos \left (y\right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 18

dsolve((2*x*y(x)^4+sin(y(x)))+ (4*x^2*y(x)^3+x*cos(y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ x^{2} y^{4}+x \sin \left (y\right )+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.201 (sec). Leaf size: 20

DSolve[(2*x*y[x]^4+Sin[y[x]])+ (4*x^2*y[x]^3+x*Cos[y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [x^2 y(x)^4+x \sin (y(x))=c_1,y(x)\right ] \]