The answer to 7 should be yCx23 dr 075r Solution5given drds

Solution

5)given dr_/ds =0.75r

seperate the variables

dr_/r =0.75 ds

integrate on both sides

dr_/r =0.75 ds

ln(r)=0.75s +c

r=e^{0.75s +c}

r=e^0.75se^c

r=Ce^0.75s

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7)

(2+x)y\'=3y

(2+x)dy_/dx=3y

seperate the variables

dy_/y=3_/(2+x) dx

integrate on both sides

dy_/y=3_/(2+x) dx

ln(y)=3ln(2+x) +c

ln(y)=ln(2+x)³ +c

y=e^{ln(2+x)^3 +c}

y=e^{ln(2+x)^3}e^c

y=e^ce^{ln(2+x)^3}

y=C(2+x)³