Internal problem ID [1999]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (5 x +y-7\right ) y^{\prime }-3-3 x -3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.284 (sec). Leaf size: 327
dsolve((5*x+y(x)-7)*diff(y(x),x)=3*(x+y(x)+1),y(x), singsol=all)
\[ y \relax (x ) = -3+\frac {144 \left (-2+x \right ) \left (-\frac {\left (1-216 \left (-2+x \right )^{2} c_{1}+12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}{24}-\frac {1}{24 \left (1-216 \left (-2+x \right )^{2} c_{1}+12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}-\frac {11}{12}+\frac {i \sqrt {3}\, \left (\frac {\left (1-216 \left (-2+x \right )^{2} c_{1}+12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}{12}-\frac {1}{12 \left (1-216 \left (-2+x \right )^{2} c_{1}+12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}\right )}{2}\right )}{-6 \left (1-216 \left (-2+x \right )^{2} c_{1}+12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}-\frac {6}{\left (1-216 \left (-2+x \right )^{2} c_{1}+12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}+12+72 i \sqrt {3}\, \left (\frac {\left (1-216 \left (-2+x \right )^{2} c_{1}+12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}{12}-\frac {1}{12 \left (1-216 \left (-2+x \right )^{2} c_{1}+12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}\right )} \]
✓ Solution by Mathematica
Time used: 0.166 (sec). Leaf size: 629
DSolve[(5*x+y[x]-7)*y'[x]==3*(x+y[x]+1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -5 x+\frac {6 (x-2)}{-\frac {1}{\sqrt [3]{-e^{\frac {3 c_1}{4}} (x-2)^4+2 e^{\frac {3 c_1}{8}} (x-2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x-2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x-2)^2\right ){}^3}-1}}+\frac {\sqrt [3]{-e^{\frac {3 c_1}{4}} (x-2)^4+2 e^{\frac {3 c_1}{8}} (x-2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x-2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x-2)^2\right ){}^3}-1}}{(x-2)^2 \cosh \left (\frac {3 c_1}{8}\right )+(x-2)^2 \sinh \left (\frac {3 c_1}{8}\right )-1}+1}+7 \\ y(x)\to -5 x+\frac {12 (x-2)}{\frac {1+i \sqrt {3}}{\sqrt [3]{-e^{\frac {3 c_1}{4}} (x-2)^4+2 e^{\frac {3 c_1}{8}} (x-2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x-2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x-2)^2\right ){}^3}-1}}+\frac {i \left (\sqrt {3}+i\right ) \sqrt [3]{-e^{\frac {3 c_1}{4}} (x-2)^4+2 e^{\frac {3 c_1}{8}} (x-2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x-2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x-2)^2\right ){}^3}-1}}{(x-2)^2 \cosh \left (\frac {3 c_1}{8}\right )+(x-2)^2 \sinh \left (\frac {3 c_1}{8}\right )-1}+2}+7 \\ y(x)\to -5 x+\frac {12 (x-2)}{\frac {1-i \sqrt {3}}{\sqrt [3]{-e^{\frac {3 c_1}{4}} (x-2)^4+2 e^{\frac {3 c_1}{8}} (x-2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x-2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x-2)^2\right ){}^3}-1}}+\frac {\left (-1-i \sqrt {3}\right ) \sqrt [3]{-e^{\frac {3 c_1}{4}} (x-2)^4+2 e^{\frac {3 c_1}{8}} (x-2)^2+\sqrt {e^{\frac {3 c_1}{8}} (x-2)^2 \left (-1+e^{\frac {3 c_1}{8}} (x-2)^2\right ){}^3}-1}}{(x-2)^2 \cosh \left (\frac {3 c_1}{8}\right )+(x-2)^2 \sinh \left (\frac {3 c_1}{8}\right )-1}+2}+7 \\ \end{align*}