Internal problem ID [986]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-y x -x y^{\frac {3}{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 20
dsolve([diff(y(x),x)-x*y(x)=x*y(x)^(3/2),y(1) = 4],y(x), singsol=all)
\[ y \relax (x ) = \frac {4}{\left (-2+3 \,{\mathrm e}^{-\frac {\left (x -1\right ) \left (x +1\right )}{4}}\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.352 (sec). Leaf size: 55
DSolve[{y'[x]-x*y[x]==x*y[x]^(3/2),y[1]==4},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (\tanh \left (\frac {1}{8} \left (-x^2+1-8 \tanh ^{-1}(3)\right )\right )-1\right )^2 \\ y(x)\to \frac {1}{4} \left (\tanh \left (-\frac {x^2}{8}+\frac {1}{8}+\tanh ^{-1}(5)\right )-1\right )^2 \\ \end{align*}