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Тамара
ЭН
Эльмира Никулина
Ответ. dy(x)/y(x)=(2*dx)/x; Ln(C)+Ln(x^2)=Ln(y(x)); y(x)=C*x^2;
СИ
Светлана Иванушкина
Solve the separable equation ( dy(x))/( dx) = (2 y(x))/x:
Divide both sides by y(x):
(( dy(x))/( dx))/(y(x)) = 2/x
Integrate both sides with respect to x:
∫ (( dy(x))/( dx))/(y(x)) dx = ∫ 2/x dx
Evaluate the integrals:
log(y(x)) = 2 log(x)+c1, where c1 is an arbitrary constant.
Solve for y(x):
y(x) = e^(c1) x^2
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