81.3.29 problem 29

Internal problem ID [18647]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 29
Date solved : Tuesday, January 28, 2025 at 12:07:32 PM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3 x +2 y-7\right ) y^{\prime }&=2 x -3 y+6 \end{align*}

✓ Solution by Maple

Time used: 0.127 (sec). Leaf size: 33

dsolve((3*x+2*y(x)-7)*diff(y(x),x)=(2*x-3*y(x)+6),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {-\sqrt {4+2197 \left (x -\frac {9}{13}\right )^{2} c_{1}^{2}}+\left (-39 x +91\right ) c_{1}}{26 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.124 (sec). Leaf size: 65

DSolve[(3*x+2*y[x]-7)*D[y[x],x]==(2*x-3*y[x]+6),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (-\sqrt {13 x^2-18 x+49+4 c_1}-3 x+7\right ) \\ y(x)\to \frac {1}{2} \left (\sqrt {13 x^2-18 x+49+4 c_1}-3 x+7\right ) \\ \end{align*}