38.2.40 problem 40

Internal problem ID [6469]
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
Date solved : Monday, January 27, 2025 at 02:06:56 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x -2 y+1}{2 x -4 y} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.108 (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)
 

\[ y = \frac {x}{2}+\frac {\sqrt {-2 x +3}}{2} \]

✓ Solution by Mathematica

Time used: 0.120 (sec). Leaf size: 24

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

\[ y(x)\to \frac {1}{2} \left (x-i \sqrt {2 x-3}\right ) \]