Internal problem ID [14330]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {6 y \sin \left (6 y x \right )+\left (4 y^{3}+6 x \sin \left (6 y x \right )\right ) y^{\prime }=4 x^{3}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.297 (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)
\[ y \left (x \right ) = \frac {\operatorname {RootOf}\left (-1296 x^{8}-1296 \cos \left (\textit {\_Z} \right ) x^{4}+1296 x^{4}+\textit {\_Z}^{4}\right )}{6 x} \]
✓ Solution by Mathematica
Time used: 0.379 (sec). Leaf size: 33
DSolve[{(-4*x^3+6*y[x]*Sin[6*x*y[x]])+(4*y[x]^3+6*x*Sin[6*x*y[x]])*y'[x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\frac {x^4}{2}+\frac {y(x)^4}{2}-\frac {1}{2} \cos (6 x y(x))=-\frac {1}{2},y(x)\right ] \]