64.6.20 problem 20

Internal problem ID [13370]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 05:33:09 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x +7 y}{2 x -2 y} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.351 (sec). Leaf size: 18

dsolve([diff(y(x),x)=(2*x+7*y(x))/(2*x-2*y(x)),y(1) = 2],y(x), singsol=all)
 

\[ y = \frac {4 \sqrt {16-15 x}}{5}-2 x +\frac {16}{5} \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 68

DSolve[{D[y[x],x]==(2*x+7*y[x])/(2*x-2*y[x]),{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

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