75.6.15 problem 148

Internal problem ID [16771]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page 54
Problem number : 148
Date solved : Tuesday, January 28, 2025 at 09:21:59 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-y \ln \left (2\right )&=2^{\sin \left (x \right )} \left (\cos \left (x \right )-1\right ) \ln \left (2\right ) \end{align*}

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 14

dsolve(diff(y(x),x)-y(x)*ln(2)=2^(sin(x))*(cos(x)-1)*ln(2),y(x), singsol=all)
 

\[ y = 2^{x} c_{1} +2^{\sin \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.364 (sec). Leaf size: 37

DSolve[D[y[x],x]-y[x]*Log[2]==2^(Sin[x])*(Cos[x]-1)*Log[2],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2^x \left (\int _1^x2^{\sin (K[1])-K[1]} (\cos (K[1])-1) \log (2)dK[1]+c_1\right ) \]