First slide

Introduction to Differential equations

Question

$If \frac{d y}{d x} + \frac{y}{x} = x^{2} then 2 y (2) - y (1) =$

Easy

A

$\frac{9}{4}$
B

$\frac{11}{4}$
C

$\frac{13}{4}$
D

$\frac{15}{4}$

Solution

$I.F = \exp \int \frac{d x}{x} = x Solution is x y = \int x^{2} \cdot x d x = \frac{x^{4}}{4} + c$
$\begin{array}{l} x = 2 \Rightarrow 2 \cdot y (2) = \frac{16}{4} + c \\ x = 1 \Rightarrow y (1) = \frac{1}{4} + c \\ 2 y (2) - y (1) = \frac{15}{4} \end{array}$

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