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Problem 6

$$\begin{array}{ll}{3 x^{n}+5 x-2 y=0 ;} & {x(0)=…

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Problem 5

$$\begin{array}{ll}{x^{n}+y-x^{\prime}=2 t ;} & {x(3)=5, \quad x^{\prime}(3)=2} \\ {y^{\prime \prime}-x+y=-1 ;} & {y(3)=1,}\end{array}$$
$$\left[\text {Hint} : \operatorname{Set} x_{1}=x, \quad x_{2}=x^{\prime}, \quad x_{3}=y, \quad x_{4}=y^{\prime}\right]$$

Answer

$x_{1}^{\prime}=x_{2}$
$x_{2}^{\prime}(t)=x_{2}-x_{3}+2 t$
$x_{3}^{\prime}=x_{4}$
$x_{4}^{\prime}=x_{1}-x_{3}-1$
$x_{1}(3)=5, x_{2}(3)=2$
$x_{3}(3)=1, x_{4}(3)=-1$


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