User:Egm6321.f09.Team8/HW2

Problem #1

Given

(7-1): Complete the details of case 2, when $h_{x}N=0$ to obtain $h(y)$

Solution

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Problem #2

Given

(8-3): Show that the solution of $y'+\frac{1}{x}y=x^{2}$ is $y=\frac{x^{3}}{4}+\frac{c}{x}$.

Solution

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Problem #3

Given

(9-2): Show that the L1_ODE_VC $\frac{1}{2}x^{2}y'+[x^{4}y+10]= 0$ is exact.

Solution

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Problem #4

Given

(9-3): Show that $(\frac{1}{3}x^{3})(y^{4})y'+(5x^{3}+2)(\frac{1}{5}y^{5})=0$ is an exact nonlinear, first order ODE.

Solution

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Problem #5

Given

(10-3): Show that the second exactness condition for $xyy''+x(y')^{2}+yy'=0$ is satisfied.

Solution

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Problem #6

Given

(11-2): Derive eq. 5 on p.(10-2) by differentiating eq. 3 on p.(10-1) with respect to $p=y'$.

Solution

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Problem #7

Given

(12-1): Use $\phi_{xy}=\phi_{yx}$ to obtain eq. 4 on p.(10-2).

Solution

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Problem #8

Given

(12-2): Verify exactness condition 2, equations 4&5 on p.(10-2).

Solution

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Problem #9

Given

(12-3): Verify the exactness of the ODE $\sqrt{x}y''+2xy'+3y=0$.

Solution

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