Internal problem ID [2508]
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`]]
\[ \boxed {\left (5 x +y-7\right ) y^{\prime }-3 y=3 x +3} \]
✓ Solution by Maple
Time used: 0.609 (sec). Leaf size: 217
dsolve((5*x+y(x)-7)*diff(y(x),x)=3*(x+y(x)+1),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x -5\right ) \left (i \sqrt {3}-1\right ) \left (216 \sqrt {c_{1} \left (-2+x \right )^{2} \left (-\frac {1}{108}+\left (-2+x \right )^{2} c_{1} \right )}+1-216 \left (-2+x \right )^{2} c_{1} \right )^{\frac {2}{3}}+\left (-22 x +38\right ) \left (216 \sqrt {c_{1} \left (-2+x \right )^{2} \left (-\frac {1}{108}+\left (-2+x \right )^{2} c_{1} \right )}+1-216 \left (-2+x \right )^{2} c_{1} \right )^{\frac {1}{3}}-\left (1+i \sqrt {3}\right ) \left (x -5\right )}{i \sqrt {3}\, \left (216 \sqrt {c_{1} \left (-2+x \right )^{2} \left (-\frac {1}{108}+\left (-2+x \right )^{2} c_{1} \right )}+1-216 \left (-2+x \right )^{2} c_{1} \right )^{\frac {2}{3}}-i \sqrt {3}-\left (216 \sqrt {c_{1} \left (-2+x \right )^{2} \left (-\frac {1}{108}+\left (-2+x \right )^{2} c_{1} \right )}+1-216 \left (-2+x \right )^{2} c_{1} \right )^{\frac {2}{3}}+2 \left (216 \sqrt {c_{1} \left (-2+x \right )^{2} \left (-\frac {1}{108}+\left (-2+x \right )^{2} c_{1} \right )}+1-216 \left (-2+x \right )^{2} c_{1} \right )^{\frac {1}{3}}-1} \]
✓ Solution by Mathematica
Time used: 60.172 (sec). Leaf size: 1626
DSolve[(5*x+y[x]-7)*y'[x]==3*(x+y[x]+1),y[x],x,IncludeSingularSolutions -> True]
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