Question
Download Solution PDFThe particular solution of \(\rm \log \frac{d y}{d x}=3 x+4 y\), y(0) = 0 is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
log \(\frac{dy}{dx}\) = 3x + 4y
\(\frac{dy}{dx}\) = e3x+4y
dy ⋅ e-4y = e3x dx
\(\int\) e-4y dy = \(\int\) e3x dx
\(\frac{e^{-4y}}{-4}\) = \(\frac{e^{3x}}{3}\) + c
when x = 0, y = 0
\(\frac{1}{-4}\) = \(\frac{1}{3}\) + c
c = \(\frac{-7}{12}\)
\(\frac{e^{-4y}}{-4}\) = \(\frac{e^{3x}}{3}\) - \(\frac{7}{12}\)
-3e-4y = 4e3x - 7
4e3x + 3e-4y = 7
Hence option 4 is correct
Last updated on Jul 3, 2025
->Vellore Institute of Technology will open its application form for 2026 on November 4, 2025.
->The VITEEE 2026 exam is scheduled to be held from April 20, 2026 to April 27, 2026.
->VITEEE exams are conduted for admission to undergraduate engineering programs at the Vellore Institute of Technology (VIT) and its affiliated campus.
->12th pass candidates can apply for the VITEEE exam.