Find the particular solution to the differential equation. (Remember to use absolute values where appropriate.) dydx=x+1xy when x=1 , y=4

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Find the particular solution to the differential equation. (Remember to use absolute values where appropriate.)  dydx=x+1xy when x=1 , y=4

Upout1940 · Accepted Answer

Step 1  Given,  dydx=x+1xy, where x=1, y=4  Step 2  Now,  ∴dydx=x+1xy  ⇒ydy=x+1xdx  Integrating both sides, we have  ⇒∫ydy=∫x+1xdx  ⇒y22=∫(x+1x)dx  ⇒y22=x22+ln|x|+C  Put x=1, y=4, then  ⇒(4)22=(1)22+ln|1|+C  ⇒8=12+C  ⇒8−12=C  ⇒C=152  The solution becomes :  ⇒y22=x22+ln|x|+152  ⇒y2=x2+2ln|x|+15  ⇒y=x2+2ln|x|+15  ∴y=x2+2ln|x|+15

Find the particular solution to the differential equation. (Remember to use absolute values where appropriate.)...

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