Internal problem ID [2050]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 18.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {\left (3 x +4 y\right ) y^{\prime }+y=-2 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve((3*x+4*y(x))*diff(y(x),x)+(y(x)+2*x)=0,y(x), singsol=all)
\[ y = \frac {x \left (\tan \left (\operatorname {RootOf}\left (\ln \left (\frac {1}{2 \cos \left (\textit {\_Z} \right )^{2}}\right )+\textit {\_Z} +2 \ln \left (x \right )+2 c_{1} \right )\right )-1\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 41
DSolve[(3*x+4*y[x])*y'[x]+(y[x]+2*x)==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\arctan \left (\frac {2 y(x)}{x}+1\right )+\log \left (\frac {2 y(x)^2}{x^2}+\frac {2 y(x)}{x}+1\right )=-2 \log (x)+c_1,y(x)\right ] \]