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Chapter 6: Q. 21 (page 570)

Use antidifferentiation and/or separation of variables to solve the given differential equations. Your answers will involve unsolved constants.

dydx=2xy

Short Answer

Expert verified

Ans: The solution of the differential equationdydx=2xyisy=Aex2

Step by step solution

01

Step 1. Given information.

given,

dydx=2xy

02

Step 2. Consider the differential equation defined by equation (1) given below and solve it by using antidifferentiation and/or separation of the variable method.  

dydx=2xy....(1)

03

Step 3. Now,

Noe that the differential equation (1)is of the form of dydx=p(x)q(y)in which p(x)=2xand q(y)=y. So the differentialequation can solved by applying variable separable method. Separate the variables and integrate both the sides

role="math" localid="1649166162207" 鈭�1ydy=鈭�2xdxln鈦�|y|=x2+Cy=ex2+C=Aex2ec=A

Hence a solution to the differential equation dydx=2xyisy=Aex2.

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