Calculus Archive: Questions from January 07, 2023
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2 answers
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Sea \( y_{1}(x)=x^{2} \cos (\ln x) \) una solución de la ecuación diferencial \( x^{2} y^{\prime \prime}-3 x y^{\prime}+5 y=0 \). Encuentre una segunda solución. \[ y_{2}(x)=x^{2} \tan (\ln x) \] \2 answers -
Encuentre la solución general de la ecuación diferencial \( \frac{d^{5} t}{d s^{5}}+5 \frac{d^{4} t}{d s^{4}}-2 \frac{d^{3} t}{d s^{3}}-10 \frac{d^{2} t}{d s^{2}}+\frac{d t}{d s}+5 t=0 \). \[ t=c_{12 answers -
What is the missing portion of \( f^{\prime} \) for \( f(x)=\frac{2 e^{\left(2 x^{2}-x\right)}}{\sqrt{3 x^{3}}+\sin ^{2} 3 x} \) ? \( (x)=\frac{\left(\sqrt{3 x^{3}}+\sin ^{2}(3 x)\right)(?)-2 e^{\left2 answers -
Evaluate the following integrals: (a) \( \int e^{2 x} \cos (3 x) d x \) (b) \( \int \frac{-3 x^{4}-24 x^{2}-16}{x^{4}-4 x^{3}+8 x^{2}} d x \)1 answer -
Evaluate the following triple integrals: a) \( \quad \int_{1}^{2} \int_{0}^{2 z} \int_{0}^{\ln x} x e^{-y} d y d x d z \) b) \( \iiint_{E} 2 x d V, E=\left\{(x, y, z) \mid 0 \leq y \leq 2,0 \leq x \le2 answers