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# Solution - Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0. - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

ConceptGeneral and Particular Solutions of a Differential Equation

#### Question

Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0.

#### Solution

dy/dx=1/cos(x+y)

Substitute x + y = v...(1)
Differentiating w.r.t. 'x', we get

1+dy/dx=(dv)/dx

dy/dx=(dv)/dx-1

The original differential equation becomes

(dv)/dx-1=1/cosv

(dv)/dx=(1+cosv)/cosv

int(cosvdv)/(1+cosv)=intdx

int((cosv+1-1)dv)/(1+cosv)=x+C

int(1+cosv)/(1+cosv)dv-int1/(1+cosv)dv=x+C

intdv-int1/(2cos^2(v/2))dv=x+C

v-1/2intsec^2(v/2)dv=x+C

v-1/2tan(v/2)dv=x+C

Resubstituting the value of 'v' from (1), we get

x+y-1/2tan((x+y)/2)=x+C

y=1/2tan((x+y)/2)=x+C

For x = 0 and y= 0, we get C=0

Hence, particular solution is y=1/2tan((x+y)/2)

Is there an error in this question or solution?

#### APPEARS IN

2015-2016 (March) (with solutions)
Question 6.2.1 | 4 marks

#### Reference Material

Solution for question: Solve the differential equation cos(x +y) dy = dx hence find the particular solution for x = 0 and y = 0. concept: General and Particular Solutions of a Differential Equation. For the courses HSC Science (Computer Science), HSC Science (Electronics), HSC Arts, HSC Science (General)
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