18.1.23 problem Problem 14.28

Internal problem ID [3479]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number : Problem 14.28
Date solved : Monday, January 27, 2025 at 07:38:33 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (5 x +y-7\right ) y^{\prime }&=3 x +3 y+3 \end{align*}

✓ Solution by Maple

Time used: 0.712 (sec). Leaf size: 210

dsolve((5*x+y(x)-7)*diff(y(x),x)=3*(x+y(x)+1),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (x -5\right ) \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{2}/{3}} \left (\sqrt {3}+i\right )-2 i \left (-11 x +19\right ) \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{1}/{3}}+\left (x -5\right ) \left (i-\sqrt {3}\right )}{\sqrt {3}\, \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{2}/{3}}-\sqrt {3}+i \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{2}/{3}}-2 i \left (216 \sqrt {\left (x -2\right )^{2} c_{1} \left (-\frac {1}{108}+\left (x -2\right )^{2} c_{1} \right )}+1-216 \left (x -2\right )^{2} c_{1} \right )^{{1}/{3}}+i} \]

✓ Solution by Mathematica

Time used: 60.184 (sec). Leaf size: 1626

DSolve[(5*x+y[x]-7)*D[y[x],x]==3*(x+y[x]+1),y[x],x,IncludeSingularSolutions -> True]
 

Too large to display