<item ident="F3-1825" title="F3 | Techniques for linear IVPs | ver. 1825"> <itemmetadata> <qtimetadata> <qtimetadatafield> <fieldlabel>question_type</fieldlabel> <fieldentry>essay_question</fieldentry> </qtimetadatafield> </qtimetadata> </itemmetadata> <presentation> <material> <mattextxml> <div class="exercise-statement"> <p> <strong>F3.</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?-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" alt="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" title="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" data-latex="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1"/> </p> </div> </mattextxml> <mattext texttype="text/html"><div class="exercise-statement"> <p> <strong>F3.</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?-%7By'%7D%20t%20+%203%20%5C,%20%7By%7D%20=%20-%5Cfrac%7B8%7D%7Bt%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%201" alt="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" title="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" data-latex="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1"> </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} = t^{3} - \frac{2}{t}" alt="{y} = t^{3} - \frac{2}{t}" title="{y} = t^{3} - \frac{2}{t}" data-latex="{y} = t^{3} - \frac{2}{t}"/> </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=%20t%5E%7B3%7D%20-%20%5Cfrac%7B2%7D%7Bt%7D" alt="{y} = t^{3} - \frac{2}{t}" title="{y} = t^{3} - \frac{2}{t}" data-latex="{y} = t^{3} - \frac{2}{t}"> </p> </div> </mattext> </material> </flow_mat> </itemfeedback> </item>