81.3.30 problem 30

Internal problem ID [18648]
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 : 30
Date solved : Tuesday, January 28, 2025 at 12:07:36 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (6 x -5 y+4\right ) y^{\prime }&=2 x -y+1 \end{align*}

✓ Solution by Maple

Time used: 0.465 (sec). Leaf size: 46

dsolve((6*x-5*y(x)+4)*diff(y(x),x)=2*x-y(x)+1,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (-4 x -1\right ) \operatorname {RootOf}\left (-3+\left (320 c_{1} x^{3}+240 c_{1} x^{2}+60 c_{1} x +5 c_{1} \right ) \textit {\_Z}^{4}-\textit {\_Z} \right )}{20}+\frac {2 x}{5}+\frac {3}{5} \]

✓ Solution by Mathematica

Time used: 60.148 (sec). Leaf size: 4977

DSolve[(6*x-5*y[x]+4)*D[y[x],x]==2*x-y[x]+1,y[x],x,IncludeSingularSolutions -> True]
 

Too large to display