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: 0.563 (sec). Leaf size: 327
dsolve((5*x+y(x)-7)*diff(y(x),x)=3*(x+y(x)+1),y(x), singsol=all)
\[ y \left (x \right ) = -3+\frac {144 \left (-2+x \right ) \left (-\frac {\left (1-216 \left (-2+x \right )^{2} c_{1} +12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}{24}-\frac {1}{24 \left (1-216 \left (-2+x \right )^{2} c_{1} +12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}-\frac {11}{12}+\frac {i \sqrt {3}\, \left (\frac {\left (1-216 \left (-2+x \right )^{2} c_{1} +12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}{12}-\frac {1}{12 \left (1-216 \left (-2+x \right )^{2} c_{1} +12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}\right )}{2}\right )}{-6 \left (1-216 \left (-2+x \right )^{2} c_{1} +12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}-\frac {6}{\left (1-216 \left (-2+x \right )^{2} c_{1} +12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}+12+72 i \sqrt {3}\, \left (\frac {\left (1-216 \left (-2+x \right )^{2} c_{1} +12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}{12}-\frac {1}{12 \left (1-216 \left (-2+x \right )^{2} c_{1} +12 \sqrt {324 \left (-2+x \right )^{4} c_{1}^{2}-3 \left (-2+x \right )^{2} c_{1}}\right )^{\frac {1}{3}}}\right )} \]
✓ Solution by Mathematica
Time used: 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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