12.5.12 problem 8

Internal problem ID [1636]
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 : 8
Date solved : Monday, January 27, 2025 at 05:15:21 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }-y x&=x y^{{3}/{2}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.062 (sec). Leaf size: 21

dsolve([diff(y(x),x)-x*y(x)=x*y(x)^(3/2),y(1) = 4],y(x), singsol=all)
 

\[ y = \frac {4}{\left (-2+3 \,{\mathrm e}^{-\frac {\left (x -1\right ) \left (x +1\right )}{4}}\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.376 (sec). Leaf size: 71

DSolve[{D[y[x],x]-x*y[x]==x*y[x]^(3/2),y[1]==4},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {4 e^{\frac {x^2}{2}}}{\left (\sqrt [4]{e}-2 e^{\frac {x^2}{4}}\right )^2} \\ y(x)\to \frac {4 e^{\frac {x^2}{2}}}{\left (3 \sqrt [4]{e}-2 e^{\frac {x^2}{4}}\right )^2} \\ \end{align*}