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CBSE Class 12 · 2007 · Differential EquationsVery Short Answer

Solve the following differential equation:

x cos y d y = (x e^{x} lo g x + e^{x}) d x

.

Answer: $sin y = e^{x} lo g x + C$

Solution

Divide by

x

to separate the variables:

cos y d y = (e^{x} lo g x + \frac{e ^{x}}{x}) d x

Notice the right side is an exact derivative, since

\frac{d}{d x} (e^{x} lo g x) = e^{x} lo g x + \frac{e ^{x}}{x}

.
Integrate both sides:

\int cos y d y = \int \frac{d}{d x} (e^{x} lo g x) d x

sin y = e^{x} lo g x + C

CBSE Class 12 Board · 2007 · Subjective

Practise more: all CBSE board PYQs on Differential Equations →

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