74.6.41 problem 42

Internal problem ID [16064]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 42
Date solved : Tuesday, January 28, 2025 at 08:34:22 AM
CAS classification : [_exact]

\begin{align*} -4 x^{3}+6 y \sin \left (6 y x \right )+\left (4 y^{3}+6 x \sin \left (6 y x \right )\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.436 (sec). Leaf size: 31

dsolve([(-4*x^3+6*y(x)*sin(6*x*y(x)))+(4*y(x)^3+6*x*sin(6*x*y(x)))*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\operatorname {RootOf}\left (-1296 x^{8}-1296 \cos \left (\textit {\_Z} \right ) x^{4}+1296 x^{4}+\textit {\_Z}^{4}\right )}{6 x} \]

✓ Solution by Mathematica

Time used: 0.415 (sec). Leaf size: 87

DSolve[{(-4*x^3+6*y[x]*Sin[6*x*y[x]])+(4*y[x]^3+6*x*Sin[6*x*y[x]])*D[y[x],x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _0^x\left (3 \sin (6 K[1] y(x)) y(x)-2 K[1]^3\right )dK[1]+\int _0^{y(x)}\left (2 K[2]^3+3 x \sin (6 x K[2])-\int _0^x(18 \cos (6 K[1] K[2]) K[1] K[2]+3 \sin (6 K[1] K[2]))dK[1]\right )dK[2]=0,y(x)\right ] \]