83.19.1 problem 1

Internal problem ID [19229]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IV. Equations of the first order but not of the first degree. Exercise IV (B) at page 55
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:14:38 PM
CAS classification : [_separable]

\begin{align*} y&=3 x +a \ln \left (y^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.028 (sec). Leaf size: 55

dsolve(y(x)=3*x+a*ln(diff(y(x),x)),y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= 3 x +a \ln \left (3\right ) \\ y \left (x \right ) &= a \ln \left (\frac {{\mathrm e}^{\frac {3 c_{1} -3 x}{a}}}{-1+{\mathrm e}^{\frac {3 c_{1} -3 x}{a}}}\right )+a \ln \left (3\right )+3 x \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.745 (sec). Leaf size: 29

DSolve[y[x]==3*x+a*Log[D[y[x],x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -a \log \left (\frac {1}{3} e^{-\frac {3 x}{a}}-\frac {c_1}{a}\right ) \]