Internal problem ID [4618]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 40.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x -2 y+1}{2 x -4 y}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.115 (sec). Leaf size: 17
dsolve([diff(y(x),x)=(x-2*y(x)+1)/(2*x-4*y(x)),y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{2}+\frac {\sqrt {-2 x +3}}{2} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 24
DSolve[{y'[x]==(x-2*y[x]+1)/(2*x-4*y[x]),{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (x-i \sqrt {2 x-3}\right ) \\ \end{align*}