Calculus Archive: Questions from January 16, 2023
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2 answers
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2 answers
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Q.6. If \( y=e^{a x} \sin b x \) then show that \( \frac{d^{2} y}{d x^{2}}-2 a \frac{d y}{d x}+\left(a^{2}+b^{2}\right) y=0 \)2 answers -
3. Solve the equation \( x y^{\prime \prime}+y^{\prime}+4 x y=0 ; y(0)=3, y^{\prime}(0)=0 \). 4. Solve the system \( \left\{\begin{array}{l}x^{\prime}(t)=y+1 \\ y^{\prime}(t)=x+t\end{array} ; x(0)=A,2 answers