38.2.6 problem 6

Internal problem ID [6435]
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 : 6
Date solved : Monday, January 27, 2025 at 02:02:59 PM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (2 y-x \right ) y^{\prime }&=y+2 x \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 51

dsolve((2*y(x)-x)*diff(y(x),x)=2*x+y(x),y(x), singsol=all)
 

\begin{align*} y &= \frac {c_1 x -\sqrt {5 x^{2} c_1^{2}+4}}{2 c_1} \\ y &= \frac {c_1 x +\sqrt {5 x^{2} c_1^{2}+4}}{2 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.456 (sec). Leaf size: 102

DSolve[(2*y[x]-x)*D[y[x],x]==2*x+y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (x-\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x+\sqrt {5 x^2-4 e^{c_1}}\right ) \\ y(x)\to \frac {1}{2} \left (x-\sqrt {5} \sqrt {x^2}\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {5} \sqrt {x^2}+x\right ) \\ \end{align*}