Direct Solution of <svg style="vertical-align:-0.216pt;width:30.325001px;" id="M1" height="16.35" version="1.1" viewBox="0 0 30.325001 16.35" width="30.325001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.022,-0,0,-.022,.062,16.025)"><path id="x1D45B" d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" /></g><g transform="matrix(.022,-0,0,-.022,11.315,16.025)"><path id="x74" d="M298 36l-68 -35q-25 -13 -42 -13q-98 0 -98 119v290h-69l-4 11l28 29h45v72l65 67l14 -2v-137h113q8 -8 6 -21t-12 -19h-107v-256q0 -96 59 -96q29 0 61 17z" /></g><g transform="matrix(.022,-0,0,-.022,18.264,16.025)"><path id="x68" d="M513 0h-211v26q44 5 55 17t11 60v166q0 123 -98 123q-59 0 -104 -51v-238q0 -48 10 -60.5t55 -16.5v-26h-213l1 26q46 4 57 16t11 61v477q0 48 -9.5 58.5t-58.5 14.5v24q63 9 147 35v-336q73 73 143 73q64 0 101 -42t37 -129v-175q0 -49 11 -61t55 -16v-26z" /></g></svg>-Order IVPs by Homotopy Analysis Method

<table>The <svg height="10.95" id="M145" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 9.1750002 10.95" width="9.1750002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.95)">
<g transform="translate(72,-63.24)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">ℏ</tspan>
</text>
</g>
</g>
</svg>-curve of <svg height="15.325" id="M146" style="vertical-align:-2.21957pt" version="1.1" viewbox="0 0 35 15.325" width="35" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.325)">
<g transform="translate(72,-59.74)">
<text transform="matrix(1,0,0,-1,-71.95,62)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,67.01)">
<tspan style="font-size: 8.75px; " x="0" y="0"></tspan>
<tspan style="font-size: 8.75px; " x="2.9756801" y="0"></tspan>
</text>
<text transform="matrix(1,0,0,-1,-58.62,62)">
<tspan style="font-size: 12.50px; " x="0" y="0">(</tspan>
<tspan style="font-size: 12.50px; " x="4.1634989" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="10.414999" y="0">)</tspan>
</text>
</g>
</g>
</svg> obtained from the eleventh-order HAM approximation solution of (<a href="https://static.hindawi.com/articles/ijde/volume-2009/842094/figures/#EEq48">3.35</a>).</table>

International Journal of Differential Equations

fig2

Figure 2

Figure 2: Direct Solution of <svg style="vertical-align:-0.216pt;width:30.325001px;" id="M1" height="16.35" version="1.1" viewBox="0 0 30.325001 16.35" width="30.325001" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.022,-0,0,-.022,.062,16.025)"><path id="x1D45B" d="M495 86q-46 -47 -87 -72.5t-63 -25.5q-43 0 -16 107l49 210q7 34 8 50.5t-3 21t-13 4.5q-35 0 -109.5 -72.5t-115.5 -140.5q-21 -75 -38 -159q-50 -10 -76 -21l-6 8l84 340q8 35 -4 35q-17 0 -67 -46l-15 26q44 44 85.5 70.5t64.5 26.5q35 0 10 -103l-24 -98h2
q42 56 97 103.5t96 71.5q46 26 74 26q9 0 16 -2.5t14 -11.5t9.5 -24.5t-1 -44t-13.5 -68.5q-30 -117 -47 -200q-4 -19 -3.5 -25t6.5 -6q21 0 70 48z" /></g><g transform="matrix(.022,-0,0,-.022,11.315,16.025)"><path id="x74" d="M298 36l-68 -35q-25 -13 -42 -13q-98 0 -98 119v290h-69l-4 11l28 29h45v72l65 67l14 -2v-137h113q8 -8 6 -21t-12 -19h-107v-256q0 -96 59 -96q29 0 61 17z" /></g><g transform="matrix(.022,-0,0,-.022,18.264,16.025)"><path id="x68" d="M513 0h-211v26q44 5 55 17t11 60v166q0 123 -98 123q-59 0 -104 -51v-238q0 -48 10 -60.5t55 -16.5v-26h-213l1 26q46 4 57 16t11 61v477q0 48 -9.5 58.5t-58.5 14.5v24q63 9 147 35v-336q73 73 143 73q64 0 101 -42t37 -129v-175q0 -49 11 -61t55 -16v-26z" /></g></svg>-Order IVPs by Homotopy Analysis Method 

International Journal of Differential Equations

Direct Solution of -Order IVPs by Homotopy Analysis Method

Figure 2