Share

# Find the Particular Solution of the Differential Equation Dy/Dx + 2y Tan X = Sin X Given that Y = 0 When X = Pi/3 - CBSE (Commerce) Class 12 - Mathematics

ConceptMethods of Solving First Order, First Degree Differential Equations Differential Equations with Variables Separable

#### Question

Find the particular solution of the differential equation dy/dx + 2y tan x = sin x given that y = 0 when x =  pi/3

#### Solution

The given differential equation is,

dy/dx + 2y tanx = sinx .....(1)

The above is a linear differential equation of the form of dy/dx + Py  = Q

where P = 2 tan x; Q = sin x

Now, If = e^(intPdx) = e^(int2tanxdx) = e^(2log sec x) = sec^2 x

Now, the solution of (1) is given by

y xx IF = int [Q xx IF]dx + C

=> ysec^2 x = int[sin x xx sec^2x] dx + C

=> y sec^2 x = intsecx.tan x dx + C

when x = pi/3 , y = 3

0 = 2 + C

C = -2

Particular solution

ysec^2x = sec x - 2

Is there an error in this question or solution?

#### APPEARS IN

Solution Find the Particular Solution of the Differential Equation Dy/Dx + 2y Tan X = Sin X Given that Y = 0 When X = Pi/3 Concept: Methods of Solving First Order, First Degree Differential Equations - Differential Equations with Variables Separable.
S