<item ident="F2-7535" title="F2 | Separation of variables | ver. 7535"> <itemmetadata> <qtimetadata> <qtimetadatafield> <fieldlabel>question_type</fieldlabel> <fieldentry>essay_question</fieldentry> </qtimetadatafield> </qtimetadata> </itemmetadata> <presentation> <material> <mattextxml> <div class="exercise-statement"> <p> <strong>F2.</strong> </p> <p>Find the solution to the given IVP.</p> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" alt="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" title="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" data-latex="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}"/> </p> </div> </mattextxml> <mattext texttype="text/html"><div class="exercise-statement"> <p> <strong>F2.</strong> </p> <p>Find the solution to the given IVP.</p> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?2%20%5C,%20%7By%7D%20%7B%5Cleft(4%20%5C,%20t%20-%201%5Cright)%7D%20+%202%20%5C,%20%7By'%7D%20=%200%20%5Chspace%7B2em%7D%20y(%200%20)=%20-2%20%5C,%20e%5E%7B2%7D" alt="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" title="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" data-latex="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}"> </p> </div> </mattext> </material> <response_str ident="response1" rcardinality="Single"> <render_fib> <response_label ident="answer1" rshuffle="No"/> </render_fib> </response_str> </presentation> <itemfeedback ident="general_fb"> <flow_mat> <material> <mattextxml> <div class="exercise-answer"> <h4>Partial Answer:</h4> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" alt="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" title="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" data-latex="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}"/> </p> </div> </mattextxml> <mattext texttype="text/html"><div class="exercise-answer"> <h4>Partial Answer:</h4> <p style="text-align:center;"> <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20=%20-2%20%5C,%20e%5E%7B%5Cleft(-2%20%5C,%20t%5E%7B2%7D%20+%20t%20+%202%5Cright)%7D" alt="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" title="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" data-latex="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}"> </p> </div> </mattext> </material> </flow_mat> </itemfeedback> </item>