HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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# Solution - Solve the differential equation dy/dx -y =e^x - HSC Science (Electronics) 12th Board Exam - Mathematics and Statistics

ConceptGeneral and Particular Solutions of a Differential Equation

#### Question

Solve the differential equation dy/dx -y =e^x

#### Solution

dy/dx -y =e^x

The given equation is of the form dy/dx+Py=Q

Where, P=-1 and Q=e^x

I.F=e^(intpdx)=e^(int-1dx)=e^-x

Solution of the given equation is

y(I.F)=intQ(I.F) dx +c

y.e^-x=inte^x.e^-xdx+c

ye^-x=x+c

put x = 0 and y = 1, we get
c = 1

y.e^(-x)=x+1

y = (x + 1) e^x is a particular solution of D.E.

Is there an error in this question or solution?

#### APPEARS IN

2016-2017 (July) (with solutions)
Question 6.2.1 | 4 marks

#### Reference Material

Solution for question: Solve the differential equation dy/dx -y =e^x concept: General and Particular Solutions of a Differential Equation. For the courses HSC Science (Electronics), HSC Science (Computer Science), HSC Science (General) , HSC Arts
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