Internal problem ID [989]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable
Equations. Section 2.4 Page 68
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }-4 y-\frac {48 x}{y^{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.053 (sec). Leaf size: 17
dsolve([diff(y(x),x)-4*y(x)=48*x/y(x)^2,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \left (2 \,{\mathrm e}^{12 x}-12 x -1\right )^{\frac {1}{3}} \]
✓ Solution by Mathematica
Time used: 0.441 (sec). Leaf size: 21
DSolve[{y'[x]-4*y[x]==48*x/y[x]^2,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{-12 x+2 e^{12 x}-1} \\ \end{align*}