73.7.24 problem 24

Internal problem ID [15182]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 07:40:29 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 24

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

\[ y = \tan \left (\operatorname {RootOf}\left (-4 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 36

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]-2}{K[1]^2+1}dK[1]=-\log (x)+c_1,y(x)\right ] \]