15.8.18 problem 18

Internal problem ID [3021]
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
Date solved : Monday, January 27, 2025 at 07:09:00 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (3 x +4 y\right ) y^{\prime }+y+2 x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 29

dsolve((3*x+4*y(x))*diff(y(x),x)+(y(x)+2*x)=0,y(x), singsol=all)
 

\[ y = \frac {x \left (\tan \left (\operatorname {RootOf}\left (-\ln \left (2\right )+\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+\textit {\_Z} +2 \ln \left (x \right )+2 c_{1} \right )\right )-1\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 41

DSolve[(3*x+4*y[x])*D[y[x],x]+(y[x]+2*x)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\arctan \left (\frac {2 y(x)}{x}+1\right )+\log \left (\frac {2 y(x)^2}{x^2}+\frac {2 y(x)}{x}+1\right )=-2 \log (x)+c_1,y(x)\right ] \]