Internal problem ID [5287]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 25 (k).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational]
\[ \boxed {y x^{3}+y+\left (x +4 y^{4} x +8 y^{3}\right ) y^{\prime }=-2 x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve((y(x)+x^3*y(x)+2*x^2)+(x+4*x*y(x)^4+8*y(x)^3)*diff(y(x),x)=0,y(x), singsol=all)
\[ -\frac {x^{3}}{3}-\ln \left (y x +2\right )-y^{4}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.188 (sec). Leaf size: 25
DSolve[(y[x]+x^3*y[x]+2*x^2)+(x+4*x*y[x]^4+8*y[x]^3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {x^3}{3}+y(x)^4+\log (x y(x)+2)=c_1,y(x)\right ] \]