Internal problem ID [11642]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {-5 y+\left (4 x -y\right ) y^{\prime }=-2 x} \] With initial conditions \begin {align*} [y \left (1\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.297 (sec). Leaf size: 35
dsolve([(2*x-5*y(x))+(4*x-y(x))*diff(y(x),x)=0,y(1) = 4],y(x), singsol=all)
\begin{align*} y \left (x \right ) = 6-2 x -6 \sqrt {1-x} y \left (x \right ) = 6-2 x +6 \sqrt {1-x} \end{align*}
✓ Solution by Mathematica
Time used: 2.199 (sec). Leaf size: 41
DSolve[{(2*x-5*y[x])+(4*x-y[x])*y'[x]==0,{y[1]==4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -2 x-6 i \sqrt {x-1}+6 y(x)\to -2 x+6 i \sqrt {x-1}+6 \end{align*}