Find the solution of the differential equation that satisfies the given initial

facas9

facas9

Answered question

2021-10-18

Find the solution of the differential equation that satisfies the given initial condition. dy/dx=x/y,y(0)=3

Answer & Explanation

Nathaniel Kramer

Nathaniel Kramer

Skilled2021-10-19Added 78 answers

Step 1 
 dy  dx =xy 
We can integrate it and rewrite it in differential notation:
xdx=ydy 
x dx =y dy  
12x2+c=12y2 
y2=x2+C 
y=±x2+c 
initial value of y is negative and square root is always positive.
y=x2+C 
Since y(0)=-3 
y(0)=02+C=3 
C=9 
y=x2+9 
Result 
y=x2+9

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