Advanced Math Archive: Questions from February 05, 2023
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2 answers
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If \( J(y)=\int_{0}^{1}\left(x^{2}-y^{2}+y^{\prime 2}\right) d x, y \in C^{2}[0,1] \), calculate \( \Delta J \) and \( \delta J(y, h) \), when \( y(x)=x \) and \( h(x)= \) \( x^{2} \)2 answers -
De la lectura 3: 3.2, 3.5, 3.6, 3.7, 3.14, 3.15, \( 3.16 \) \( 3.2 \) Encontrar la solución general para \( x y^{\prime \prime}+y^{\prime}=0 \). Hint: Se puede convertir a una de primer orden. 3.5 En3 answers -
write the differential equation in standard form of a first order system of differential equations
(4) Escribu la ecwación dif. en la forma sto. de un sissena Le ecuaciones diff de primer ode. \[ \left(\frac{d^{3} y}{d t^{3}}\right)^{2}+t^{2} \frac{d^{2} y}{d t^{2}}+\frac{d y}{d t}-y=4 t \]2 answers -
\( \begin{array}{lr}\text { cond. } & y\left(\pi(\pi)^{1 / 4}\right)=1 \\ y & \left.=1(\pi / 4)^{\prime \prime}\right)=2 \\ x^{2} y^{\prime \prime}-5 x y^{\prime}+\left(64 x^{8}+5\right) y=0\end{array2 answers -
2 answers