12.5.15 problem 11

Internal problem ID [1639]
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
Date solved : Monday, January 27, 2025 at 05:15:34 AM
CAS classification : [_rational, _Bernoulli]

\begin{align*} y^{\prime }-4 y&=\frac {48 x}{y^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 17

dsolve([diff(y(x),x)-4*y(x)=48*x/y(x)^2,y(0) = 1],y(x), singsol=all)
 

\[ y = \left (2 \,{\mathrm e}^{12 x}-12 x -1\right )^{{1}/{3}} \]

✓ Solution by Mathematica

Time used: 4.527 (sec). Leaf size: 21

DSolve[{D[y[x],x]-4*y[x]==48*x/y[x]^2,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt [3]{-12 x+2 e^{12 x}-1} \]