Internal problem ID [5029]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems.
page 12
Problem number: 32.
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 {y^{\prime }+\frac {4 x +3 y+15}{2 x +y+7}=0} \end {gather*}
✓ Solution by Maple
Time used: 1.391 (sec). Leaf size: 204
dsolve(diff(y(x),x)=-(4*x+3*y(x)+15)/(2*x+y(x)+7),y(x), singsol=all)
\[ y \relax (x ) = -1-\frac {\frac {\left (-\frac {1}{2}+\frac {i \sqrt {3}}{2}\right )^{6} \left (-2 \left (4 \left (3+x \right )^{3} c_{1}+4 \sqrt {-4 \left (3+x \right )^{9} c_{1}^{3}+\left (3+x \right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}-\frac {8 \left (3+x \right )^{3} c_{1}}{\left (4 \left (3+x \right )^{3} c_{1}+4 \sqrt {-4 \left (3+x \right )^{9} c_{1}^{3}+\left (3+x \right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}}+4 i \sqrt {3}\, \left (\frac {\left (4 \left (3+x \right )^{3} c_{1}+4 \sqrt {-4 \left (3+x \right )^{9} c_{1}^{3}+\left (3+x \right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}}{2}-\frac {2 \left (3+x \right )^{3} c_{1}}{\left (4 \left (3+x \right )^{3} c_{1}+4 \sqrt {-4 \left (3+x \right )^{9} c_{1}^{3}+\left (3+x \right )^{6} c_{1}^{2}}\right )^{\frac {1}{3}}}\right )\right )^{2}}{64 c_{1}}+\left (3+x \right )^{3}}{\left (3+x \right )^{2}} \]
✓ Solution by Mathematica
Time used: 60.109 (sec). Leaf size: 763
DSolve[y'[x]==-(4*x+3*y[x]+15)/(2*x+y[x]+7),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,1\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,2\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,3\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,4\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,5\right ]}-2 x-7 \\ y(x)\to \frac {1}{\text {Root}\left [\text {$\#$1}^6 \left (16 x^6+288 x^5+2160 x^4+8640 x^3+19440 x^2+23328 x+11664+16 e^{12 c_1}\right )+\text {$\#$1}^4 \left (-24 x^4-288 x^3-1296 x^2-2592 x-1944\right )+\text {$\#$1}^3 \left (-8 x^3-72 x^2-216 x-216\right )+\text {$\#$1}^2 \left (9 x^2+54 x+81\right )+\text {$\#$1} (6 x+18)+1\&,6\right ]}-2 x-7 \\ \end{align*}